2x+16=12x+x^2

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

2x+16=12x+x^2

We move all terms to the left:

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

We get rid of parentheses

-x^2-12x+2x+16=0

We add all the numbers together, and all the variables

-1x^2-10x+16=0

a = -1; b = -10; c = +16;
Δ = b2-4ac
Δ = -102-4·(-1)·16
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{41}}{2*-1}=\frac{10-2\sqrt{41}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{41}}{2*-1}=\frac{10+2\sqrt{41}}{-2}
$