(24+x)*(600-12*x)=0

Solution for (24+x)*(600-12*x)=0 equation:

(24+x)(600-12x)=0

We add all the numbers together, and all the variables

(x+24)(-12x+600)=0

We multiply parentheses ..

(-12x^2+600x-288x+14400)=0

We get rid of parentheses

-12x^2+600x-288x+14400=0

We add all the numbers together, and all the variables

-12x^2+312x+14400=0

a = -12; b = 312; c = +14400;
Δ = b2-4ac
Δ = 3122-4·(-12)·14400
Δ = 788544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{788544}=888$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(312)-888}{2*-12}=\frac{-1200}{-24}
=+50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(312)+888}{2*-12}=\frac{576}{-24}
=-24
$