6x^2-27=39

Solution for 6x^2-27=39 equation:

6x^2-27=39

We move all terms to the left:

6x^2-27-(39)=0

We add all the numbers together, and all the variables

6x^2-66=0

a = 6; b = 0; c = -66;
Δ = b2-4ac
Δ = 02-4·6·(-66)
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{11}}{2*6}=\frac{0-12\sqrt{11}}{12}
=-\frac{12\sqrt{11}}{12}
=-\sqrt{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{11}}{2*6}=\frac{0+12\sqrt{11}}{12}
=\frac{12\sqrt{11}}{12}
=\sqrt{11}
$