20x^2=100x+120

Solution for 20x^2=100x+120 equation:

20x^2=100x+120

We move all terms to the left:

20x^2-(100x+120)=0

We get rid of parentheses

20x^2-100x-120=0

a = 20; b = -100; c = -120;
Δ = b2-4ac
Δ = -1002-4·20·(-120)
Δ = 19600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19600}=140$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-140}{2*20}=\frac{-40}{40}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+140}{2*20}=\frac{240}{40}
=6
$