2x+1/2x=54

Solution for 2x+1/2x=54 equation:

2x+1/2x=54

We move all terms to the left:

2x+1/2x-(54)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


2x*2x-54*2x+1=0

Wy multiply elements

4x^2-108x+1=0

a = 4; b = -108; c = +1;
Δ = b2-4ac
Δ = -1082-4·4·1
Δ = 11648
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:

$\sqrt{\Delta}=\sqrt{11648}=\sqrt{64*182}=\sqrt{64}*\sqrt{182}=8\sqrt{182}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-8\sqrt{182}}{2*4}=\frac{108-8\sqrt{182}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+8\sqrt{182}}{2*4}=\frac{108+8\sqrt{182}}{8}
$