4(x-5)(2x+5)=0

Solution for 4(x-5)(2x+5)=0 equation:

4(x-5)(2x+5)=0

We multiply parentheses ..

4(+2x^2+5x-10x-25)=0

We multiply parentheses

8x^2+20x-40x-100=0

We add all the numbers together, and all the variables

8x^2-20x-100=0

a = 8; b = -20; c = -100;
Δ = b2-4ac
Δ = -202-4·8·(-100)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-60}{2*8}=\frac{-40}{16}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+60}{2*8}=\frac{80}{16}
=5
$