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

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

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

We multiply parentheses ..

(+40x^2+20x-48x-24)=0

We get rid of parentheses

40x^2+20x-48x-24=0

We add all the numbers together, and all the variables

40x^2-28x-24=0

a = 40; b = -28; c = -24;
Δ = b2-4ac
Δ = -282-4·40·(-24)
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-68}{2*40}=\frac{-40}{80}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+68}{2*40}=\frac{96}{80}
=1+1/5
$