100=x^2+3x^2

Solution for 100=x^2+3x^2 equation:

100=x^2+3x^2

We move all terms to the left:

100-(x^2+3x^2)=0

We get rid of parentheses

-x^2-3x^2+100=0

We add all the numbers together, and all the variables

-4x^2+100=0

a = -4; b = 0; c = +100;
Δ = b2-4ac
Δ = 02-4·(-4)·100
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40}{2*-4}=\frac{-40}{-8}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40}{2*-4}=\frac{40}{-8}
=-5
$