2x+9/2x=26

Solution for 2x+9/2x=26 equation:

2x+9/2x=26

We move all terms to the left:

2x+9/2x-(26)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


2x*2x-26*2x+9=0

Wy multiply elements

4x^2-52x+9=0

a = 4; b = -52; c = +9;
Δ = b2-4ac
Δ = -522-4·4·9
Δ = 2560
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:

$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-16\sqrt{10}}{2*4}=\frac{52-16\sqrt{10}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+16\sqrt{10}}{2*4}=\frac{52+16\sqrt{10}}{8}
$