(10+4x)(2400-200x)=0

Solution for (10+4x)(2400-200x)=0 equation:

(10+4x)(2400-200x)=0

We add all the numbers together, and all the variables

(4x+10)(-200x+2400)=0

We multiply parentheses ..

(-800x^2+9600x-2000x+24000)=0

We get rid of parentheses

-800x^2+9600x-2000x+24000=0

We add all the numbers together, and all the variables

-800x^2+7600x+24000=0

a = -800; b = 7600; c = +24000;
Δ = b2-4ac
Δ = 76002-4·(-800)·24000
Δ = 134560000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{134560000}=11600$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7600)-11600}{2*-800}=\frac{-19200}{-1600}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7600)+11600}{2*-800}=\frac{4000}{-1600}
=-2+1/2
$