120x^2-20x-75=0

Solution for 120x^2-20x-75=0 equation:

120x^2-20x-75=0

a = 120; b = -20; c = -75;
Δ = b2-4ac
Δ = -202-4·120·(-75)
Δ = 36400
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:

$\sqrt{\Delta}=\sqrt{36400}=\sqrt{400*91}=\sqrt{400}*\sqrt{91}=20\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{91}}{2*120}=\frac{20-20\sqrt{91}}{240}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{91}}{2*120}=\frac{20+20\sqrt{91}}{240}
$