(X^2)-12x+12=1056

Solution for (X^2)-12x+12=1056 equation:

(X^2)-12X+12=1056

We move all terms to the left:

(X^2)-12X+12-(1056)=0

We add all the numbers together, and all the variables

X^2-12X-1044=0

a = 1; b = -12; c = -1044;
Δ = b2-4ac
Δ = -122-4·1·(-1044)
Δ = 4320
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:

$\sqrt{\Delta}=\sqrt{4320}=\sqrt{144*30}=\sqrt{144}*\sqrt{30}=12\sqrt{30}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{30}}{2*1}=\frac{12-12\sqrt{30}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{30}}{2*1}=\frac{12+12\sqrt{30}}{2}
$