84=-31+x2

Solution for 84=-31+x2 equation:

84=-31+x2

We move all terms to the left:

84-(-31+x2)=0

We add all the numbers together, and all the variables

-(+x^2-31)+84=0

We get rid of parentheses

-x^2+31+84=0

We add all the numbers together, and all the variables

-1x^2+115=0

a = -1; b = 0; c = +115;
Δ = b2-4ac
Δ = 02-4·(-1)·115
Δ = 460
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:

$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{115}}{2*-1}=\frac{0-2\sqrt{115}}{-2}
=-\frac{2\sqrt{115}}{-2}
=-\frac{\sqrt{115}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{115}}{2*-1}=\frac{0+2\sqrt{115}}{-2}
=\frac{2\sqrt{115}}{-2}
=\frac{\sqrt{115}}{-1}
$