-4x^2-4x+124=52

Solution for -4x^2-4x+124=52 equation:

-4x^2-4x+124=52

We move all terms to the left:

-4x^2-4x+124-(52)=0

We add all the numbers together, and all the variables

-4x^2-4x+72=0

a = -4; b = -4; c = +72;
Δ = b2-4ac
Δ = -42-4·(-4)·72
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{73}}{2*-4}=\frac{4-4\sqrt{73}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{73}}{2*-4}=\frac{4+4\sqrt{73}}{-8}
$