3x^2-27x+6=0

Solution for 3x^2-27x+6=0 equation:

3x^2-27x+6=0

a = 3; b = -27; c = +6;
Δ = b2-4ac
Δ = -272-4·3·6
Δ = 657
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:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{73}}{2*3}=\frac{27-3\sqrt{73}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{73}}{2*3}=\frac{27+3\sqrt{73}}{6}
$