22x-x^2-120=0

Solution for 22x-x^2-120=0 equation:

22x-x^2-120=0

We add all the numbers together, and all the variables

-1x^2+22x-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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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