9x^2-54x-27=0

Solution for 9x^2-54x-27=0 equation:

9x^2-54x-27=0

a = 9; b = -54; c = -27;
Δ = b2-4ac
Δ = -542-4·9·(-27)
Δ = 3888
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:

$\sqrt{\Delta}=\sqrt{3888}=\sqrt{1296*3}=\sqrt{1296}*\sqrt{3}=36\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-36\sqrt{3}}{2*9}=\frac{54-36\sqrt{3}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+36\sqrt{3}}{2*9}=\frac{54+36\sqrt{3}}{18}
$