First we want to put the equation into standard form; we do this by making sure the equation is = 0, so let's subtract 4 from both sides.

We could go straight to the quadratic formula from here, but quadratics are always easier to solve if we eliminate Greatest Common Factors first. In this case the GCF is 4 so let's divide both sides by 4.

Now we can compare against the standard form to find a, b, and c.

By pattern matching, we see that a = 1, b = -3, and c = 4. Now we substitute into the quadratic formula.

We can evaluate the square root of a negative number by factoring out the square root of -1 and calling it the imaginary number i. This gives our answer.

Since the equation is already in standard form, we can compare it to the general version of standard form to find a, b, and c.

By pattern matching it is clear that a = 2, b = 4, and c = -3. Now we can substitute into the quadratic formula.

Recall that when subtracting a negative number [as in - 4(2)(-3)], the result is addition:

Combine terms and simplify the radical:

Now eliminate common factors to reduce to lowest terms.

We begin by designating values of a, b and c by comparing the equation to the standard form.

By pattern matching it is clear that a = 2, b = -3, and c = -5. We can now substitute into the quadratic formula:

Take note that in the two cases where negatives/minus signs are multiplied together [-(-3) and -4(2)(-5)], they bceome positive:

Now we simplify and evaluate.

Note that in the previous step we listed the subtraction instance first, as that instance yields the smaller number and it is usually convenient to start sets with smaller numbers first. 

Recall that the quadratic formula is defined as:

For this question, the variables are as follows:

Substituting these values into the equation, you get:

Since you have to take the square root of a negative number, this means that there are no real solutions.

Recall that the quadratic formula is defined as:

For this question, the variables are as follows:

Substituting these values into the equation, you get:

Use a calculator to determine the final values.

Recall that the quadratic formula is defined as:

For this question, the variables are as follows:

Substituting these values into the equation, you get:

Use a calculator to determine the final values.

Recall that the quadratic formula is defined as:

For this question, the variables are as follows:

Substituting these values into the equation, you get:

Separate this expression into two fractions and simplify to determine the final values.

Recall that the quadratic formula is defined as:

For this question, the variables are as follows:

Substituting these values into the equation, you get:

Separate this expression into two fractions and simplify to determine the final values.

Based on the quadratic equation:

,

, , and 

Given the quadratic formula:

We have:

Simplfying,

We use the quadratic equation to solve for x. The quadratic equation is:

In our case 

Substituting these values into the quadratic equation we get: