3x^2+500^2=7x^2

Solution for 3x^2+500^2=7x^2 equation:

3x^2+500^2=7x^2

We move all terms to the left:

3x^2+500^2-(7x^2)=0

We add all the numbers together, and all the variables

-4x^2+250000=0

a = -4; b = 0; c = +250000;
Δ = b2-4ac
Δ = 02-4·(-4)·250000
Δ = 4000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4000000}=2000$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2000}{2*-4}=\frac{-2000}{-8}
=+250
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2000}{2*-4}=\frac{2000}{-8}
=-250
$