0=5x^2+8x-7

Solution for 0=5x^2+8x-7 equation:

0=5x^2+8x-7

We move all terms to the left:

0-(5x^2+8x-7)=0

We add all the numbers together, and all the variables

-(5x^2+8x-7)=0

We get rid of parentheses

-5x^2-8x+7=0

a = -5; b = -8; c = +7;
Δ = b2-4ac
Δ = -82-4·(-5)·7
Δ = 204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{51}}{2*-5}=\frac{8-2\sqrt{51}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{51}}{2*-5}=\frac{8+2\sqrt{51}}{-10}
$