6(24x^2-24x-18)=0

Solution for 6(24x^2-24x-18)=0 equation:

6(24x^2-24x-18)=0

We multiply parentheses

144x^2-144x-108=0

a = 144; b = -144; c = -108;
Δ = b2-4ac
Δ = -1442-4·144·(-108)
Δ = 82944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{82944}=288$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-288}{2*144}=\frac{-144}{288}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+288}{2*144}=\frac{432}{288}
=1+1/2
$