x^2-2x-16=12x

Solution for x^2-2x-16=12x equation:

x^2-2x-16=12x

We move all terms to the left:

x^2-2x-16-(12x)=0

We add all the numbers together, and all the variables

x^2-14x-16=0

a = 1; b = -14; c = -16;
Δ = b2-4ac
Δ = -142-4·1·(-16)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{65}}{2*1}=\frac{14-2\sqrt{65}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{65}}{2*1}=\frac{14+2\sqrt{65}}{2}
$