31=x^2+17

Solution for 31=x^2+17 equation:

31=x^2+17

We move all terms to the left:

31-(x^2+17)=0

We get rid of parentheses

-x^2-17+31=0

We add all the numbers together, and all the variables

-1x^2+14=0

a = -1; b = 0; c = +14;
Δ = b2-4ac
Δ = 02-4·(-1)·14
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{14}}{2*-1}=\frac{0-2\sqrt{14}}{-2}
=-\frac{2\sqrt{14}}{-2}
=-\frac{\sqrt{14}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{14}}{2*-1}=\frac{0+2\sqrt{14}}{-2}
=\frac{2\sqrt{14}}{-2}
=\frac{\sqrt{14}}{-1}
$