(120-10x)(10+3x)=0

Solution for (120-10x)(10+3x)=0 equation:

(120-10x)(10+3x)=0

We add all the numbers together, and all the variables

(-10x+120)(3x+10)=0

We multiply parentheses ..

(-30x^2-100x+360x+1200)=0

We get rid of parentheses

-30x^2-100x+360x+1200=0

We add all the numbers together, and all the variables

-30x^2+260x+1200=0

a = -30; b = 260; c = +1200;
Δ = b2-4ac
Δ = 2602-4·(-30)·1200
Δ = 211600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{211600}=460$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(260)-460}{2*-30}=\frac{-720}{-60}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(260)+460}{2*-30}=\frac{200}{-60}
=-3+1/3
$