x2+12x=6

Solution for x2+12x=6 equation:

x2+12x=6

We move all terms to the left:

x2+12x-(6)=0

We add all the numbers together, and all the variables

x^2+12x-6=0

a = 1; b = 12; c = -6;
Δ = b2-4ac
Δ = 122-4·1·(-6)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{42}}{2*1}=\frac{-12-2\sqrt{42}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{42}}{2*1}=\frac{-12+2\sqrt{42}}{2}
$