100/31=x2-100

Solution for 100/31=x2-100 equation:

100/31=x2-100

We move all terms to the left:

100/31-(x2-100)=0

We add all the numbers together, and all the variables

-(+x^2-100)+100/31=0

We get rid of parentheses

-x^2+100+100/31=0

We multiply all the terms by the denominator


-x^2*31+100+100*31=0

We add all the numbers together, and all the variables

-x^2*31+3200=0

Wy multiply elements

-31x^2+3200=0

a = -31; b = 0; c = +3200;
Δ = b2-4ac
Δ = 02-4·(-31)·3200
Δ = 396800
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:

$\sqrt{\Delta}=\sqrt{396800}=\sqrt{6400*62}=\sqrt{6400}*\sqrt{62}=80\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{62}}{2*-31}=\frac{0-80\sqrt{62}}{-62}
=-\frac{80\sqrt{62}}{-62}
=-\frac{40\sqrt{62}}{-31}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{62}}{2*-31}=\frac{0+80\sqrt{62}}{-62}
=\frac{80\sqrt{62}}{-62}
=\frac{40\sqrt{62}}{-31}
$