(5x-8)(3x+8)=0

Solution for (5x-8)(3x+8)=0 equation:

(5x-8)(3x+8)=0

We multiply parentheses ..

(+15x^2+40x-24x-64)=0

We get rid of parentheses

15x^2+40x-24x-64=0

We add all the numbers together, and all the variables

15x^2+16x-64=0

a = 15; b = 16; c = -64;
Δ = b2-4ac
Δ = 162-4·15·(-64)
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-64}{2*15}=\frac{-80}{30}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+64}{2*15}=\frac{48}{30}
=1+3/5
$