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

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

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

We multiply parentheses ..

(+40x^2+25x-64x-40)=0

We get rid of parentheses

40x^2+25x-64x-40=0

We add all the numbers together, and all the variables

40x^2-39x-40=0

a = 40; b = -39; c = -40;
Δ = b2-4ac
Δ = -392-4·40·(-40)
Δ = 7921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7921}=89$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-89}{2*40}=\frac{-50}{80}
=-5/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+89}{2*40}=\frac{128}{80}
=1+3/5
$