6x^2+6=12x+18

Solution for 6x^2+6=12x+18 equation:

6x^2+6=12x+18

We move all terms to the left:

6x^2+6-(12x+18)=0

We get rid of parentheses

6x^2-12x-18+6=0

We add all the numbers together, and all the variables

6x^2-12x-12=0

a = 6; b = -12; c = -12;
Δ = b2-4ac
Δ = -122-4·6·(-12)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{3}}{2*6}=\frac{12-12\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{3}}{2*6}=\frac{12+12\sqrt{3}}{12}
$