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 = 1944
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:

$\sqrt{\Delta}=\sqrt{1944}=\sqrt{324*6}=\sqrt{324}*\sqrt{6}=18\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-18\sqrt{6}}{2*9}=\frac{54-18\sqrt{6}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+18\sqrt{6}}{2*9}=\frac{54+18\sqrt{6}}{18}
$