0=9x^2-29x+22

Solution for 0=9x^2-29x+22 equation:

0=9x^2-29x+22

We move all terms to the left:

0-(9x^2-29x+22)=0

We add all the numbers together, and all the variables

-(9x^2-29x+22)=0

We get rid of parentheses

-9x^2+29x-22=0

a = -9; b = 29; c = -22;
Δ = b2-4ac
Δ = 292-4·(-9)·(-22)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-7}{2*-9}=\frac{-36}{-18}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+7}{2*-9}=\frac{-22}{-18}
=1+2/9
$