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

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

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

We multiply parentheses ..

6(+3x^2+8x-18x-48)=0

We multiply parentheses

18x^2+48x-108x-288=0

We add all the numbers together, and all the variables

18x^2-60x-288=0

a = 18; b = -60; c = -288;
Δ = b2-4ac
Δ = -602-4·18·(-288)
Δ = 24336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24336}=156$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-156}{2*18}=\frac{-96}{36}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+156}{2*18}=\frac{216}{36}
=6
$