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

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

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

We multiply parentheses ..

(+8x^2+40x-2x-10)=0

We get rid of parentheses

8x^2+40x-2x-10=0

We add all the numbers together, and all the variables

8x^2+38x-10=0

a = 8; b = 38; c = -10;
Δ = b2-4ac
Δ = 382-4·8·(-10)
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*8}=\frac{-80}{16}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+42}{2*8}=\frac{4}{16}
=1/4
$