SOLUTION: Find the discriminant and solutions for the following equations 5x^2+4x-3=0 please do a step by step :-)

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Question 872756: Find the discriminant and solutions for the following equations 5x^2+4x-3=0 please do a step by step :-)
Found 2 solutions by richwmiller, rfer:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B4x%2B-3+=+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=%284%29%5E2-4%2A5%2A-3=76.

Discriminant d=76 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+76+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+76+%29%29%2F2%5C5+=+0.471779788708135
x%5B2%5D+=+%28-%284%29-sqrt%28+76+%29%29%2F2%5C5+=+-1.27177978870813

Quadratic expression 5x%5E2%2B4x%2B-3 can be factored:
5x%5E2%2B4x%2B-3+=+5%28x-0.471779788708135%29%2A%28x--1.27177978870813%29
Again, the answer is: 0.471779788708135, -1.27177978870813. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B4%2Ax%2B-3+%29

Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
a=5, b=4, c=-3
----------------
discriminant
b^2-4ac
12-4*5*-3
12+60=72
-------------
sqrt 72=8.49
----------------
(-4+-8.49)/10
-12/10=-1.2 (-1.2,0)
+4.49/10=(0.45,0)
---------------
vertex
-4/10=-0.4 =x
5*-0.4^2+4*-0.4-3=-3.8
(-0.4,-3.8)