Y=x^2+22x+120

Solution for Y=x^2+22x+120 equation:

=Y^2+22Y+120

We move all terms to the left:

-(Y^2+22Y+120)=0

We get rid of parentheses

-Y^2-22Y-120=0

We add all the numbers together, and all the variables

-1Y^2-22Y-120=0

a = -1; b = -22; c = -120;
Δ = b2-4ac
Δ = -222-4·(-1)·(-120)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2}{2*-1}=\frac{20}{-2}
=-10
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2}{2*-1}=\frac{24}{-2}
=-12
$