6x(x-3)=6x+18

Solution for 6x(x-3)=6x+18 equation:

6x(x-3)=6x+18

We move all terms to the left:

6x(x-3)-(6x+18)=0

We multiply parentheses

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

We get rid of parentheses

6x^2-18x-6x-18=0

We add all the numbers together, and all the variables

6x^2-24x-18=0

a = 6; b = -24; c = -18;
Δ = b2-4ac
Δ = -242-4·6·(-18)
Δ = 1008
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{7}}{2*6}=\frac{24-12\sqrt{7}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{7}}{2*6}=\frac{24+12\sqrt{7}}{12}
$