(8x-5)(6x+8)=0

Solution for (8x-5)(6x+8)=0 equation:

(8x-5)(6x+8)=0

We multiply parentheses ..

(+48x^2+64x-30x-40)=0

We get rid of parentheses

48x^2+64x-30x-40=0

We add all the numbers together, and all the variables

48x^2+34x-40=0

a = 48; b = 34; c = -40;
Δ = b2-4ac
Δ = 342-4·48·(-40)
Δ = 8836
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8836}=94$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-94}{2*48}=\frac{-128}{96}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+94}{2*48}=\frac{60}{96}
=5/8
$