(x-8)(4x+10)=0

Solution for (x-8)(4x+10)=0 equation:

(x-8)(4x+10)=0

We multiply parentheses ..

(+4x^2+10x-32x-80)=0

We get rid of parentheses

4x^2+10x-32x-80=0

We add all the numbers together, and all the variables

4x^2-22x-80=0

a = 4; b = -22; c = -80;
Δ = b2-4ac
Δ = -222-4·4·(-80)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-42}{2*4}=\frac{-20}{8}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+42}{2*4}=\frac{64}{8}
=8
$