4+x^2=25x^2

Solution for 4+x^2=25x^2 equation:

4+x^2=25x^2

We move all terms to the left:

4+x^2-(25x^2)=0

We add all the numbers together, and all the variables

-24x^2+4=0

a = -24; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-24)·4
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{6}}{2*-24}=\frac{0-8\sqrt{6}}{-48}
=-\frac{8\sqrt{6}}{-48}
=-\frac{\sqrt{6}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{6}}{2*-24}=\frac{0+8\sqrt{6}}{-48}
=\frac{8\sqrt{6}}{-48}
=\frac{\sqrt{6}}{-6}
$