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

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

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

We multiply parentheses ..

(+5x^2+10x-8x-16)=0

We get rid of parentheses

5x^2+10x-8x-16=0

We add all the numbers together, and all the variables

5x^2+2x-16=0

a = 5; b = 2; c = -16;
Δ = b2-4ac
Δ = 22-4·5·(-16)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-18}{2*5}=\frac{-20}{10}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+18}{2*5}=\frac{16}{10}
=1+3/5
$