(X-2)(x-2)=169

Solution for (X-2)(x-2)=169 equation:

(X-2)(X-2)=169

We move all terms to the left:

(X-2)(X-2)-(169)=0

We multiply parentheses ..

(+X^2-2X-2X+4)-169=0

We get rid of parentheses

X^2-2X-2X+4-169=0

We add all the numbers together, and all the variables

X^2-4X-165=0

a = 1; b = -4; c = -165;
Δ = b2-4ac
Δ = -42-4·1·(-165)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-26}{2*1}=\frac{-22}{2}
=-11
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+26}{2*1}=\frac{30}{2}
=15
$