2x+1/2x=27.5

Solution for 2x+1/2x=27.5 equation:

2x+1/2x=27.5

We move all terms to the left:

2x+1/2x-(27.5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/2x-27.5=0

We multiply all the terms by the denominator


2x*2x-(27.5)*2x+1=0

We multiply parentheses

2x*2x-55x+1=0

Wy multiply elements

4x^2-55x+1=0

a = 4; b = -55; c = +1;
Δ = b2-4ac
Δ = -552-4·4·1
Δ = 3009
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-\sqrt{3009}}{2*4}=\frac{55-\sqrt{3009}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{3009}}{2*4}=\frac{55+\sqrt{3009}}{8}
$