20x+x^2=120

Solution for 20x+x^2=120 equation:

20x+x^2=120

We move all terms to the left:

20x+x^2-(120)=0

a = 1; b = 20; c = -120;
Δ = b2-4ac
Δ = 202-4·1·(-120)
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{55}}{2*1}=\frac{-20-4\sqrt{55}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{55}}{2*1}=\frac{-20+4\sqrt{55}}{2}
$