x^2-31=16

Solution for x^2-31=16 equation:

x^2-31=16

We move all terms to the left:

x^2-31-(16)=0

We add all the numbers together, and all the variables

x^2-47=0

a = 1; b = 0; c = -47;
Δ = b2-4ac
Δ = 02-4·1·(-47)
Δ = 188
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:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{47}}{2*1}=\frac{0-2\sqrt{47}}{2}
=-\frac{2\sqrt{47}}{2}
=-\sqrt{47}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{47}}{2*1}=\frac{0+2\sqrt{47}}{2}
=\frac{2\sqrt{47}}{2}
=\sqrt{47}
$