(5x+8)(12x-6)=0

Solution for (5x+8)(12x-6)=0 equation:

(5x+8)(12x-6)=0

We multiply parentheses ..

(+60x^2-30x+96x-48)=0

We get rid of parentheses

60x^2-30x+96x-48=0

We add all the numbers together, and all the variables

60x^2+66x-48=0

a = 60; b = 66; c = -48;
Δ = b2-4ac
Δ = 662-4·60·(-48)
Δ = 15876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15876}=126$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-126}{2*60}=\frac{-192}{120}
=-1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+126}{2*60}=\frac{60}{120}
=1/2
$