(x-5)*(x-5)=9

Solution for (x-5)*(x-5)=9 equation:

(x-5)(x-5)=9

We move all terms to the left:

(x-5)(x-5)-(9)=0

We multiply parentheses ..

(+x^2-5x-5x+25)-9=0

We get rid of parentheses

x^2-5x-5x+25-9=0

We add all the numbers together, and all the variables

x^2-10x+16=0

a = 1; b = -10; c = +16;
Δ = b2-4ac
Δ = -102-4·1·16
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6}{2*1}=\frac{4}{2}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6}{2*1}=\frac{16}{2}
=8
$