12x^2-80x-100=0

Solution for 12x^2-80x-100=0 equation:

12x^2-80x-100=0

a = 12; b = -80; c = -100;
Δ = b2-4ac
Δ = -802-4·12·(-100)
Δ = 11200
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:

$\sqrt{\Delta}=\sqrt{11200}=\sqrt{1600*7}=\sqrt{1600}*\sqrt{7}=40\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-40\sqrt{7}}{2*12}=\frac{80-40\sqrt{7}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+40\sqrt{7}}{2*12}=\frac{80+40\sqrt{7}}{24}
$