(x-7)*(x-7)=6

Solution for (x-7)*(x-7)=6 equation:

(x-7)(x-7)=6

We move all terms to the left:

(x-7)(x-7)-(6)=0

We multiply parentheses ..

(+x^2-7x-7x+49)-6=0

We get rid of parentheses

x^2-7x-7x+49-6=0

We add all the numbers together, and all the variables

x^2-14x+43=0

a = 1; b = -14; c = +43;
Δ = b2-4ac
Δ = -142-4·1·43
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{6}}{2*1}=\frac{14-2\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{6}}{2*1}=\frac{14+2\sqrt{6}}{2}
$