(5x-4)(8x+6)=0

Solution for (5x-4)(8x+6)=0 equation:

(5x-4)(8x+6)=0

We multiply parentheses ..

(+40x^2+30x-32x-24)=0

We get rid of parentheses

40x^2+30x-32x-24=0

We add all the numbers together, and all the variables

40x^2-2x-24=0

a = 40; b = -2; c = -24;
Δ = b2-4ac
Δ = -22-4·40·(-24)
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-62}{2*40}=\frac{-60}{80}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+62}{2*40}=\frac{64}{80}
=4/5
$