(10x+50)(-3x+24)=0

Solution for (10x+50)(-3x+24)=0 equation:

(10x+50)(-3x+24)=0

We multiply parentheses ..

(-30x^2+240x-150x+1200)=0

We get rid of parentheses

-30x^2+240x-150x+1200=0

We add all the numbers together, and all the variables

-30x^2+90x+1200=0

a = -30; b = 90; c = +1200;
Δ = b2-4ac
Δ = 902-4·(-30)·1200
Δ = 152100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{152100}=390$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-390}{2*-30}=\frac{-480}{-60}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+390}{2*-30}=\frac{300}{-60}
=-5
$