3x^2-27x-27=0

Solution for 3x^2-27x-27=0 equation:

3x^2-27x-27=0

a = 3; b = -27; c = -27;
Δ = b2-4ac
Δ = -272-4·3·(-27)
Δ = 1053
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:

$\sqrt{\Delta}=\sqrt{1053}=\sqrt{81*13}=\sqrt{81}*\sqrt{13}=9\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-9\sqrt{13}}{2*3}=\frac{27-9\sqrt{13}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+9\sqrt{13}}{2*3}=\frac{27+9\sqrt{13}}{6}
$