0=8x^2+24x-568

Solution for 0=8x^2+24x-568 equation:

0=8x^2+24x-568

We move all terms to the left:

0-(8x^2+24x-568)=0

We add all the numbers together, and all the variables

-(8x^2+24x-568)=0

We get rid of parentheses

-8x^2-24x+568=0

a = -8; b = -24; c = +568;
Δ = b2-4ac
Δ = -242-4·(-8)·568
Δ = 18752
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:

$\sqrt{\Delta}=\sqrt{18752}=\sqrt{64*293}=\sqrt{64}*\sqrt{293}=8\sqrt{293}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{293}}{2*-8}=\frac{24-8\sqrt{293}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{293}}{2*-8}=\frac{24+8\sqrt{293}}{-16}
$