(x+8)(5x-2)=0

Solution for (x+8)(5x-2)=0 equation:

(x+8)(5x-2)=0

We multiply parentheses ..

(+5x^2-2x+40x-16)=0

We get rid of parentheses

5x^2-2x+40x-16=0

We add all the numbers together, and all the variables

5x^2+38x-16=0

a = 5; b = 38; c = -16;
Δ = b2-4ac
Δ = 382-4·5·(-16)
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{-(38)-42}{2*5}=\frac{-80}{10}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+42}{2*5}=\frac{4}{10}
=2/5
$