(6x-3)(8x+6)=0

Solution for (6x-3)(8x+6)=0 equation:

(6x-3)(8x+6)=0

We multiply parentheses ..

(+48x^2+36x-24x-18)=0

We get rid of parentheses

48x^2+36x-24x-18=0

We add all the numbers together, and all the variables

48x^2+12x-18=0

a = 48; b = 12; c = -18;
Δ = b2-4ac
Δ = 122-4·48·(-18)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-60}{2*48}=\frac{-72}{96}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+60}{2*48}=\frac{48}{96}
=1/2
$