(4x-10)(20+5x)=0

Solution for (4x-10)(20+5x)=0 equation:

(4x-10)(20+5x)=0

We add all the numbers together, and all the variables

(4x-10)(5x+20)=0

We multiply parentheses ..

(+20x^2+80x-50x-200)=0

We get rid of parentheses

20x^2+80x-50x-200=0

We add all the numbers together, and all the variables

20x^2+30x-200=0

a = 20; b = 30; c = -200;
Δ = b2-4ac
Δ = 302-4·20·(-200)
Δ = 16900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16900}=130$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-130}{2*20}=\frac{-160}{40}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+130}{2*20}=\frac{100}{40}
=2+1/2
$