x^2+22x+33=-2

Solution for x^2+22x+33=-2 equation:

x^2+22x+33=-2

We move all terms to the left:

x^2+22x+33-(-2)=0

We add all the numbers together, and all the variables

x^2+22x+35=0

a = 1; b = 22; c = +35;
Δ = b2-4ac
Δ = 222-4·1·35
Δ = 344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{344}=\sqrt{4*86}=\sqrt{4}*\sqrt{86}=2\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{86}}{2*1}=\frac{-22-2\sqrt{86}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{86}}{2*1}=\frac{-22+2\sqrt{86}}{2}
$