9a^2-22a+4=0

Solution for 9a^2-22a+4=0 equation:

9a^2-22a+4=0

a = 9; b = -22; c = +4;
Δ = b2-4ac
Δ = -222-4·9·4
Δ = 340
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{85}}{2*9}=\frac{22-2\sqrt{85}}{18}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{85}}{2*9}=\frac{22+2\sqrt{85}}{18}
$