250(2)^2=2(x)^2

Solution for 250(2)^2=2(x)^2 equation:

250(2)^2=2(x)^2

We move all terms to the left:

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

determiningTheFunctionDomain
-2x^2+2502^2=0

We add all the numbers together, and all the variables

-2x^2+6260004=0

a = -2; b = 0; c = +6260004;
Δ = b2-4ac
Δ = 02-4·(-2)·6260004
Δ = 50080032
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:

$\sqrt{\Delta}=\sqrt{50080032}=\sqrt{25040016*2}=\sqrt{25040016}*\sqrt{2}=5004\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-5004\sqrt{2}}{2*-2}=\frac{0-5004\sqrt{2}}{-4}
=-\frac{5004\sqrt{2}}{-4}
=-\frac{1251\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+5004\sqrt{2}}{2*-2}=\frac{0+5004\sqrt{2}}{-4}
=\frac{5004\sqrt{2}}{-4}
=\frac{1251\sqrt{2}}{-1}
$