(X-9)(x-9)=324

Solution for (X-9)(x-9)=324 equation:

(X-9)(X-9)=324

We move all terms to the left:

(X-9)(X-9)-(324)=0

We multiply parentheses ..

(+X^2-9X-9X+81)-324=0

We get rid of parentheses

X^2-9X-9X+81-324=0

We add all the numbers together, and all the variables

X^2-18X-243=0

a = 1; b = -18; c = -243;
Δ = b2-4ac
Δ = -182-4·1·(-243)
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{-(-18)-36}{2*1}=\frac{-18}{2}
=-9
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+36}{2*1}=\frac{54}{2}
=27
$