(1200-5x)(50+5x)=0

Solution for (1200-5x)(50+5x)=0 equation:

(1200-5x)(50+5x)=0

We add all the numbers together, and all the variables

(-5x+1200)(5x+50)=0

We multiply parentheses ..

(-25x^2-250x+6000x+60000)=0

We get rid of parentheses

-25x^2-250x+6000x+60000=0

We add all the numbers together, and all the variables

-25x^2+5750x+60000=0

a = -25; b = 5750; c = +60000;
Δ = b2-4ac
Δ = 57502-4·(-25)·60000
Δ = 39062500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{39062500}=6250$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5750)-6250}{2*-25}=\frac{-12000}{-50}
=+240
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5750)+6250}{2*-25}=\frac{500}{-50}
=-10
$