x^2+250x=2x^2

Solution for x^2+250x=2x^2 equation:

x^2+250x=2x^2

We move all terms to the left:

x^2+250x-(2x^2)=0

determiningTheFunctionDomain
x^2-2x^2+250x=0

We add all the numbers together, and all the variables

-1x^2+250x=0

a = -1; b = 250; c = 0;
Δ = b2-4ac
Δ = 2502-4·(-1)·0
Δ = 62500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{62500}=250$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-250}{2*-1}=\frac{-500}{-2}
=+250
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+250}{2*-1}=\frac{0}{-2}
=0
$