576=2x^2+8x-48

Solution for 576=2x^2+8x-48 equation:

576=2x^2+8x-48

We move all terms to the left:

576-(2x^2+8x-48)=0

We get rid of parentheses

-2x^2-8x+48+576=0

We add all the numbers together, and all the variables

-2x^2-8x+624=0

a = -2; b = -8; c = +624;
Δ = b2-4ac
Δ = -82-4·(-2)·624
Δ = 5056
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:

$\sqrt{\Delta}=\sqrt{5056}=\sqrt{64*79}=\sqrt{64}*\sqrt{79}=8\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{79}}{2*-2}=\frac{8-8\sqrt{79}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{79}}{2*-2}=\frac{8+8\sqrt{79}}{-4}
$