X(120-x)-50x=0

Solution for X(120-x)-50x=0 equation:

X(120-X)-50X=0

We add all the numbers together, and all the variables

X(-1X+120)-50X=0

We add all the numbers together, and all the variables

-50X+X(-1X+120)=0

We multiply parentheses

-1X^2-50X+120X=0

We add all the numbers together, and all the variables

-1X^2+70X=0

a = -1; b = 70; c = 0;
Δ = b2-4ac
Δ = 702-4·(-1)·0
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-70}{2*-1}=\frac{-140}{-2}
=+70
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+70}{2*-1}=\frac{0}{-2}
=0
$