(X-3)(x-3)=55

Solution for (X-3)(x-3)=55 equation:

(X-3)(X-3)=55

We move all terms to the left:

(X-3)(X-3)-(55)=0

We multiply parentheses ..

(+X^2-3X-3X+9)-55=0

We get rid of parentheses

X^2-3X-3X+9-55=0

We add all the numbers together, and all the variables

X^2-6X-46=0

a = 1; b = -6; c = -46;
Δ = b2-4ac
Δ = -62-4·1·(-46)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{55}}{2*1}=\frac{6-2\sqrt{55}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{55}}{2*1}=\frac{6+2\sqrt{55}}{2}
$