0=4x^2+24x-76

Solution for 0=4x^2+24x-76 equation:

0=4x^2+24x-76

We move all terms to the left:

0-(4x^2+24x-76)=0

We add all the numbers together, and all the variables

-(4x^2+24x-76)=0

We get rid of parentheses

-4x^2-24x+76=0

a = -4; b = -24; c = +76;
Δ = b2-4ac
Δ = -242-4·(-4)·76
Δ = 1792
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:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-16\sqrt{7}}{2*-4}=\frac{24-16\sqrt{7}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+16\sqrt{7}}{2*-4}=\frac{24+16\sqrt{7}}{-8}
$