SOLUTION: How do I find the solutions and x-intercepts of 3x^2-5x-7=0?

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Question 455108: How do I find the solutions and x-intercepts of 3x^2-5x-7=0?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
y = 3x^2-5x-7
then, set y=0 to find the x-intercepts:
0 = 3x^2-5x-7
since you can't factor the right, apply the "quadratic formula" to get:
x = {2.57, -0.91}
.
x-intercepts are at:
(2.57,0) and (-0.91,0)
.
details of quadratic follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-5x%2B-7+=+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=%28-5%29%5E2-4%2A3%2A-7=109.

Discriminant d=109 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+109+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+109+%29%29%2F2%5C3+=+2.57338441815176
x%5B2%5D+=+%28-%28-5%29-sqrt%28+109+%29%29%2F2%5C3+=+-0.906717751485092

Quadratic expression 3x%5E2%2B-5x%2B-7 can be factored:
3x%5E2%2B-5x%2B-7+=+3%28x-2.57338441815176%29%2A%28x--0.906717751485092%29
Again, the answer is: 2.57338441815176, -0.906717751485092. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-5%2Ax%2B-7+%29