9x^2-54x+81=36

Solution for 9x^2-54x+81=36 equation:

9x^2-54x+81=36

We move all terms to the left:

9x^2-54x+81-(36)=0

We add all the numbers together, and all the variables

9x^2-54x+45=0

a = 9; b = -54; c = +45;
Δ = b2-4ac
Δ = -542-4·9·45
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-36}{2*9}=\frac{18}{18}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+36}{2*9}=\frac{90}{18}
=5
$