x2+22x+117=0

Solution for x2+22x+117=0 equation:

x2+22x+117=0

We add all the numbers together, and all the variables

x^2+22x+117=0

a = 1; b = 22; c = +117;
Δ = b2-4ac
Δ = 222-4·1·117
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-4}{2*1}=\frac{-26}{2}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+4}{2*1}=\frac{-18}{2}
=-9
$