SOLUTION: (3x)(3x)+5x-12=0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: (3x)(3x)+5x-12=0      Log On


   

Question 279622: (3x)(3x)+5x-12=0
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
9x^2+5x-12=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 9x%5E2%2B5x%2B-12+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%285%29%5E2-4%2A9%2A-12=457.

Discriminant d=457 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+457+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+457+%29%29%2F2%5C9+=+0.909864351468442
x%5B2%5D+=+%28-%285%29-sqrt%28+457+%29%29%2F2%5C9+=+-1.465419907024

Quadratic expression 9x%5E2%2B5x%2B-12 can be factored:
9x%5E2%2B5x%2B-12+=+9%28x-0.909864351468442%29%2A%28x--1.465419907024%29
Again, the answer is: 0.909864351468442, -1.465419907024. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B5%2Ax%2B-12+%29