(60-2x)(120+5x)=0

Solution for (60-2x)(120+5x)=0 equation:

(60-2x)(120+5x)=0

We add all the numbers together, and all the variables

(-2x+60)(5x+120)=0

We multiply parentheses ..

(-10x^2-240x+300x+7200)=0

We get rid of parentheses

-10x^2-240x+300x+7200=0

We add all the numbers together, and all the variables

-10x^2+60x+7200=0

a = -10; b = 60; c = +7200;
Δ = b2-4ac
Δ = 602-4·(-10)·7200
Δ = 291600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{291600}=540$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-540}{2*-10}=\frac{-600}{-20}
=+30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+540}{2*-10}=\frac{480}{-20}
=-24
$