12x^2-120x-200=0

Solution for 12x^2-120x-200=0 equation:

12x^2-120x-200=0

a = 12; b = -120; c = -200;
Δ = b2-4ac
Δ = -1202-4·12·(-200)
Δ = 24000
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:

$\sqrt{\Delta}=\sqrt{24000}=\sqrt{1600*15}=\sqrt{1600}*\sqrt{15}=40\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-40\sqrt{15}}{2*12}=\frac{120-40\sqrt{15}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+40\sqrt{15}}{2*12}=\frac{120+40\sqrt{15}}{24}
$