100=x2+40

Solution for 100=x2+40 equation:

100=x2+40

We move all terms to the left:

100-(x2+40)=0

We add all the numbers together, and all the variables

-(+x^2+40)+100=0

We get rid of parentheses

-x^2-40+100=0

We add all the numbers together, and all the variables

-1x^2+60=0

a = -1; b = 0; c = +60;
Δ = b2-4ac
Δ = 02-4·(-1)·60
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*-1}=\frac{0-4\sqrt{15}}{-2}
=-\frac{4\sqrt{15}}{-2}
=-\frac{2\sqrt{15}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*-1}=\frac{0+4\sqrt{15}}{-2}
=\frac{4\sqrt{15}}{-2}
=\frac{2\sqrt{15}}{-1}
$