x^2=12x+14

Solution for x^2=12x+14 equation:

x^2=12x+14

We move all terms to the left:

x^2-(12x+14)=0

We get rid of parentheses

x^2-12x-14=0

a = 1; b = -12; c = -14;
Δ = b2-4ac
Δ = -122-4·1·(-14)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-10\sqrt{2}}{2*1}=\frac{12-10\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+10\sqrt{2}}{2*1}=\frac{12+10\sqrt{2}}{2}
$