X^2+12=31-2x

Solution for X^2+12=31-2x equation:

X^2+12=31-2X

We move all terms to the left:

X^2+12-(31-2X)=0

We add all the numbers together, and all the variables

X^2-(-2X+31)+12=0

We get rid of parentheses

X^2+2X-31+12=0

We add all the numbers together, and all the variables

X^2+2X-19=0

a = 1; b = 2; c = -19;
Δ = b2-4ac
Δ = 22-4·1·(-19)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{5}}{2*1}=\frac{-2-4\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{5}}{2*1}=\frac{-2+4\sqrt{5}}{2}
$