x^2-12x+38=90

Solution for x^2-12x+38=90 equation:

x^2-12x+38=90

We move all terms to the left:

x^2-12x+38-(90)=0

We add all the numbers together, and all the variables

x^2-12x-52=0

a = 1; b = -12; c = -52;
Δ = b2-4ac
Δ = -122-4·1·(-52)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{22}}{2*1}=\frac{12-4\sqrt{22}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{22}}{2*1}=\frac{12+4\sqrt{22}}{2}
$