x^2+2=12x+72

Solution for x^2+2=12x+72 equation:

x^2+2=12x+72

We move all terms to the left:

x^2+2-(12x+72)=0

We get rid of parentheses

x^2-12x-72+2=0

We add all the numbers together, and all the variables

x^2-12x-70=0

a = 1; b = -12; c = -70;
Δ = b2-4ac
Δ = -122-4·1·(-70)
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{106}}{2*1}=\frac{12-2\sqrt{106}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{106}}{2*1}=\frac{12+2\sqrt{106}}{2}
$