SOLUTION: How do you solve 2a^2 - 5a - 12 = 0 in quadratic form?

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Question 300474: How do you solve 2a^2 - 5a - 12 = 0 in quadratic form?
Found 2 solutions by Fombitz, JBarnum:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You can factor,
2a%5E2+-+5a+-+12+=%282a%2B3%29%28a-4%29
Two solutions:
2a%2B3=0
2a=-3
highlight_green%28+a=-3%2F2%29
.
.
.
a-4=0
highlight_green%28a=4%29
.
.
.
Graphical verification,
+graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C+2x%5E2+-+5x+-+12+%29+

Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aA%5E2%2BbA%2Bc=0 (in our case 2A%5E2%2B-5A%2B-12+=+0) has the following solutons:

A%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%2A2%2A-12=121.

Discriminant d=121 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+121+%29%29%2F2%5Ca.

A%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+121+%29%29%2F2%5C2+=+4
A%5B2%5D+=+%28-%28-5%29-sqrt%28+121+%29%29%2F2%5C2+=+-1.5

Quadratic expression 2A%5E2%2B-5A%2B-12 can be factored:
2A%5E2%2B-5A%2B-12+=+2%28A-4%29%2A%28A--1.5%29
Again, the answer is: 4, -1.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-5%2Ax%2B-12+%29