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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

40x^2-34x-48=0

a = 40; b = -34; c = -48;
Δ = b2-4ac
Δ = -342-4·40·(-48)
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*40}=\frac{-60}{80}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+94}{2*40}=\frac{128}{80}
=1+3/5
$