x=26/2x

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Solution for x=26/2x equation:



x=26/2x
We move all terms to the left:
x-(26/2x)=0
Domain of the equation: 2x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
x-(+26/2x)=0
We get rid of parentheses
x-26/2x=0
We multiply all the terms by the denominator
x*2x-26=0
Wy multiply elements
2x^2-26=0
a = 2; b = 0; c = -26;
Δ = b2-4ac
Δ = 02-4·2·(-26)
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*2}=\frac{0-4\sqrt{13}}{4} =-\frac{4\sqrt{13}}{4} =-\sqrt{13} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{13}}{2*2}=\frac{0+4\sqrt{13}}{4} =\frac{4\sqrt{13}}{4} =\sqrt{13} $

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