x^2-2(x-3)=12

Solution for x^2-2(x-3)=12 equation:

x^2-2(x-3)=12

We move all terms to the left:

x^2-2(x-3)-(12)=0

We multiply parentheses

x^2-2x+6-12=0

We add all the numbers together, and all the variables

x^2-2x-6=0

a = 1; b = -2; c = -6;
Δ = b2-4ac
Δ = -22-4·1·(-6)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{7}}{2*1}=\frac{2-2\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{7}}{2*1}=\frac{2+2\sqrt{7}}{2}
$