SOLUTION: Solve by using the quadratic formula. 3x^2 = 11x + 4

Question 88263: Solve by using the quadratic formula. 3x^2 = 11x + 4
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Get everything to one side

Now let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general form of the quadratic equation is:

So lets solve (notice , , and )

Plug in a=3, b=-11, and c=-4

Negate -11 to get 11

Square -11 to get 121

Multiply to get

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

Simplify the square root

Multiply 2 and 3 to get 6

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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