9y^2-30y+22=0

Solution for 9y^2-30y+22=0 equation:

9y^2-30y+22=0

a = 9; b = -30; c = +22;
Δ = b2-4ac
Δ = -302-4·9·22
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{3}}{2*9}=\frac{30-6\sqrt{3}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{3}}{2*9}=\frac{30+6\sqrt{3}}{18}
$