27x^2-120x+11=0

Solution for 27x^2-120x+11=0 equation:

27x^2-120x+11=0

a = 27; b = -120; c = +11;
Δ = b2-4ac
Δ = -1202-4·27·11
Δ = 13212
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:

$\sqrt{\Delta}=\sqrt{13212}=\sqrt{36*367}=\sqrt{36}*\sqrt{367}=6\sqrt{367}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-6\sqrt{367}}{2*27}=\frac{120-6\sqrt{367}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+6\sqrt{367}}{2*27}=\frac{120+6\sqrt{367}}{54}
$