SOLUTION: Solve the following quadratic equation. 4x squared = 13x + 12

Question 114388: Solve the following quadratic equation.
4x squared = 13x + 12
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation

Move all of the terms to the right side

Sort the terms

Switch both sides (I find it easier to read if all of the terms are on the left side)

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=-4, b=13, and c=12

Square 13 to get 169

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and -4 to get -8

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or

Notice when we graph , we get:

and we can see that the roots are and . This verifies our answer

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