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

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

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

We multiply parentheses ..

(+4x^2+10x-20x-50)=0

We get rid of parentheses

4x^2+10x-20x-50=0

We add all the numbers together, and all the variables

4x^2-10x-50=0

a = 4; b = -10; c = -50;
Δ = b2-4ac
Δ = -102-4·4·(-50)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-30}{2*4}=\frac{-20}{8}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+30}{2*4}=\frac{40}{8}
=5
$