x^2+3=12x-12

Solution for x^2+3=12x-12 equation:

x^2+3=12x-12

We move all terms to the left:

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

We get rid of parentheses

x^2-12x+12+3=0

We add all the numbers together, and all the variables

x^2-12x+15=0

a = 1; b = -12; c = +15;
Δ = b2-4ac
Δ = -122-4·1·15
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{21}}{2*1}=\frac{12-2\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{21}}{2*1}=\frac{12+2\sqrt{21}}{2}
$