27x^2-27x=14

Solution for 27x^2-27x=14 equation:

27x^2-27x=14

We move all terms to the left:

27x^2-27x-(14)=0

a = 27; b = -27; c = -14;
Δ = b2-4ac
Δ = -272-4·27·(-14)
Δ = 2241
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:

$\sqrt{\Delta}=\sqrt{2241}=\sqrt{9*249}=\sqrt{9}*\sqrt{249}=3\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{249}}{2*27}=\frac{27-3\sqrt{249}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{249}}{2*27}=\frac{27+3\sqrt{249}}{54}
$