12x^2-104x-120=0

Solution for 12x^2-104x-120=0 equation:

12x^2-104x-120=0

a = 12; b = -104; c = -120;
Δ = b2-4ac
Δ = -1042-4·12·(-120)
Δ = 16576
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:

$\sqrt{\Delta}=\sqrt{16576}=\sqrt{64*259}=\sqrt{64}*\sqrt{259}=8\sqrt{259}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-8\sqrt{259}}{2*12}=\frac{104-8\sqrt{259}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+8\sqrt{259}}{2*12}=\frac{104+8\sqrt{259}}{24}
$