(X-4)(x-4)=28

Solution for (X-4)(x-4)=28 equation:

(X-4)(X-4)=28

We move all terms to the left:

(X-4)(X-4)-(28)=0

We multiply parentheses ..

(+X^2-4X-4X+16)-28=0

We get rid of parentheses

X^2-4X-4X+16-28=0

We add all the numbers together, and all the variables

X^2-8X-12=0

a = 1; b = -8; c = -12;
Δ = b2-4ac
Δ = -82-4·1·(-12)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{7}}{2*1}=\frac{8-4\sqrt{7}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{7}}{2*1}=\frac{8+4\sqrt{7}}{2}
$