Y=x^2+9x-22

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

=Y^2+9Y-22

We move all terms to the left:

-(Y^2+9Y-22)=0

We get rid of parentheses

-Y^2-9Y+22=0

We add all the numbers together, and all the variables

-1Y^2-9Y+22=0

a = -1; b = -9; c = +22;
Δ = b2-4ac
Δ = -92-4·(-1)·22
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-13}{2*-1}=\frac{-4}{-2}
=+2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+13}{2*-1}=\frac{22}{-2}
=-11
$