-4x^2-80x+112=0

Solution for -4x^2-80x+112=0 equation:

-4x^2-80x+112=0

a = -4; b = -80; c = +112;
Δ = b2-4ac
Δ = -802-4·(-4)·112
Δ = 8192
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:

$\sqrt{\Delta}=\sqrt{8192}=\sqrt{4096*2}=\sqrt{4096}*\sqrt{2}=64\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-64\sqrt{2}}{2*-4}=\frac{80-64\sqrt{2}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+64\sqrt{2}}{2*-4}=\frac{80+64\sqrt{2}}{-8}
$