27x^2-6x^2-12=0

Solution for 27x^2-6x^2-12=0 equation:

27x^2-6x^2-12=0

We add all the numbers together, and all the variables

21x^2-12=0

a = 21; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·21·(-12)
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{-(0)-12\sqrt{7}}{2*21}=\frac{0-12\sqrt{7}}{42}
=-\frac{12\sqrt{7}}{42}
=-\frac{2\sqrt{7}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{7}}{2*21}=\frac{0+12\sqrt{7}}{42}
=\frac{12\sqrt{7}}{42}
=\frac{2\sqrt{7}}{7}
$