9x^2-54x+81=10

Solution for 9x^2-54x+81=10 equation:

9x^2-54x+81=10

We move all terms to the left:

9x^2-54x+81-(10)=0

We add all the numbers together, and all the variables

9x^2-54x+71=0

a = 9; b = -54; c = +71;
Δ = b2-4ac
Δ = -542-4·9·71
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{10}}{2*9}=\frac{54-6\sqrt{10}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{10}}{2*9}=\frac{54+6\sqrt{10}}{18}
$