x^2-6x+81=90

Solution for x^2-6x+81=90 equation:

x^2-6x+81=90

We move all terms to the left:

x^2-6x+81-(90)=0

We add all the numbers together, and all the variables

x^2-6x-9=0

a = 1; b = -6; c = -9;
Δ = b2-4ac
Δ = -62-4·1·(-9)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{2}}{2*1}=\frac{6-6\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{2}}{2*1}=\frac{6+6\sqrt{2}}{2}
$