x^2+4x^2=500

Solution for x^2+4x^2=500 equation:

x^2+4x^2=500

We move all terms to the left:

x^2+4x^2-(500)=0

We add all the numbers together, and all the variables

5x^2-500=0

a = 5; b = 0; c = -500;
Δ = b2-4ac
Δ = 02-4·5·(-500)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100}{2*5}=\frac{-100}{10}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100}{2*5}=\frac{100}{10}
=10
$