1/26x=2x

Solution for 1/26x=2x equation:

1/26x=2x

We move all terms to the left:

1/26x-(2x)=0


Domain of the equation: 26x!=0

x!=0/26

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+1/26x=0

We multiply all the terms by the denominator


-2x*26x+1=0

Wy multiply elements

-52x^2+1=0

a = -52; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-52)·1
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{13}}{2*-52}=\frac{0-4\sqrt{13}}{-104}
=-\frac{4\sqrt{13}}{-104}
=-\frac{\sqrt{13}}{-26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{13}}{2*-52}=\frac{0+4\sqrt{13}}{-104}
=\frac{4\sqrt{13}}{-104}
=\frac{\sqrt{13}}{-26}
$