2y^2-18y+9=0

Solution for 2y^2-18y+9=0 equation:

2y^2-18y+9=0

a = 2; b = -18; c = +9;
Δ = b2-4ac
Δ = -182-4·2·9
Δ = 252
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{7}}{2*2}=\frac{18-6\sqrt{7}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{7}}{2*2}=\frac{18+6\sqrt{7}}{4}
$