(X-7)*(x-7)=1

Solution for (X-7)*(x-7)=1 equation:

(X-7)(X-7)=1

We move all terms to the left:

(X-7)(X-7)-(1)=0

We multiply parentheses ..

(+X^2-7X-7X+49)-1=0

We get rid of parentheses

X^2-7X-7X+49-1=0

We add all the numbers together, and all the variables

X^2-14X+48=0

a = 1; b = -14; c = +48;
Δ = b2-4ac
Δ = -142-4·1·48
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2}{2*1}=\frac{12}{2}
=6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2}{2*1}=\frac{16}{2}
=8
$