8x^2=500+2x^2

Solution for 8x^2=500+2x^2 equation:

8x^2=500+2x^2

We move all terms to the left:

8x^2-(500+2x^2)=0

We get rid of parentheses

8x^2-2x^2-500=0

We add all the numbers together, and all the variables

6x^2-500=0

a = 6; b = 0; c = -500;
Δ = b2-4ac
Δ = 02-4·6·(-500)
Δ = 12000
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:

$\sqrt{\Delta}=\sqrt{12000}=\sqrt{400*30}=\sqrt{400}*\sqrt{30}=20\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{30}}{2*6}=\frac{0-20\sqrt{30}}{12}
=-\frac{20\sqrt{30}}{12}
=-\frac{5\sqrt{30}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{30}}{2*6}=\frac{0+20\sqrt{30}}{12}
=\frac{20\sqrt{30}}{12}
=\frac{5\sqrt{30}}{3}
$