-12x^2-88x-20=0

Solution for -12x^2-88x-20=0 equation:

-12x^2-88x-20=0

a = -12; b = -88; c = -20;
Δ = b2-4ac
Δ = -882-4·(-12)·(-20)
Δ = 6784
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:

$\sqrt{\Delta}=\sqrt{6784}=\sqrt{64*106}=\sqrt{64}*\sqrt{106}=8\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-8\sqrt{106}}{2*-12}=\frac{88-8\sqrt{106}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+8\sqrt{106}}{2*-12}=\frac{88+8\sqrt{106}}{-24}
$