0=16x^2+256x-624

Solution for 0=16x^2+256x-624 equation:

0=16x^2+256x-624

We move all terms to the left:

0-(16x^2+256x-624)=0

We add all the numbers together, and all the variables

-(16x^2+256x-624)=0

We get rid of parentheses

-16x^2-256x+624=0

a = -16; b = -256; c = +624;
Δ = b2-4ac
Δ = -2562-4·(-16)·624
Δ = 105472
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:

$\sqrt{\Delta}=\sqrt{105472}=\sqrt{1024*103}=\sqrt{1024}*\sqrt{103}=32\sqrt{103}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-256)-32\sqrt{103}}{2*-16}=\frac{256-32\sqrt{103}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-256)+32\sqrt{103}}{2*-16}=\frac{256+32\sqrt{103}}{-32}
$