SOLUTION: Solve using the quadratic equation {{{3x^2+2.5x=12.5}}}

Question 857661: Solve using the quadratic equation
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
3x^2+2.5x-12.5=0

Solved by pluggable solver: Quadratic Formula

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=6, b=5, and c=-25

Square 5 to get 25

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 6 to get 12

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

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=156.25 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.66666666666667, -2.5. Here's your graph:

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