6x*x-6x-18=0

Solution for 6x*x-6x-18=0 equation:

6x*x-6x-18=0

We add all the numbers together, and all the variables

-6x+6x*x-18=0

Wy multiply elements

6x^2-6x-18=0

a = 6; b = -6; c = -18;
Δ = b2-4ac
Δ = -62-4·6·(-18)
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{13}}{2*6}=\frac{6-6\sqrt{13}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{13}}{2*6}=\frac{6+6\sqrt{13}}{12}
$