(3x+4)(6x-8)=0

Solution for (3x+4)(6x-8)=0 equation:

(3x+4)(6x-8)=0

We multiply parentheses ..

(+18x^2-24x+24x-32)=0

We get rid of parentheses

18x^2-24x+24x-32=0

We add all the numbers together, and all the variables

18x^2-32=0

a = 18; b = 0; c = -32;
Δ = b2-4ac
Δ = 02-4·18·(-32)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48}{2*18}=\frac{-48}{36}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48}{2*18}=\frac{48}{36}
=1+1/3
$