x^2+120x-4200=0

Solution for x^2+120x-4200=0 equation:

x^2+120x-4200=0

a = 1; b = 120; c = -4200;
Δ = b2-4ac
Δ = 1202-4·1·(-4200)
Δ = 31200
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:

$\sqrt{\Delta}=\sqrt{31200}=\sqrt{400*78}=\sqrt{400}*\sqrt{78}=20\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-20\sqrt{78}}{2*1}=\frac{-120-20\sqrt{78}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+20\sqrt{78}}{2*1}=\frac{-120+20\sqrt{78}}{2}
$