2r^2-18r+27=0

Solution for 2r^2-18r+27=0 equation:

2r^2-18r+27=0

a = 2; b = -18; c = +27;
Δ = b2-4ac
Δ = -182-4·2·27
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{3}}{2*2}=\frac{18-6\sqrt{3}}{4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{3}}{2*2}=\frac{18+6\sqrt{3}}{4}
$