x^2+22x+120=224

Solution for x^2+22x+120=224 equation:

x^2+22x+120=224

We move all terms to the left:

x^2+22x+120-(224)=0

We add all the numbers together, and all the variables

x^2+22x-104=0

a = 1; b = 22; c = -104;
Δ = b2-4ac
Δ = 222-4·1·(-104)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-30}{2*1}=\frac{-52}{2}
=-26
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+30}{2*1}=\frac{8}{2}
=4
$