x2+12x+22=90

Solution for x2+12x+22=90 equation:

x2+12x+22=90

We move all terms to the left:

x2+12x+22-(90)=0

We add all the numbers together, and all the variables

x^2+12x-68=0

a = 1; b = 12; c = -68;
Δ = b2-4ac
Δ = 122-4·1·(-68)
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{26}}{2*1}=\frac{-12-4\sqrt{26}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{26}}{2*1}=\frac{-12+4\sqrt{26}}{2}
$