1/2x+2x=55

Solution for 1/2x+2x=55 equation:

1/2x+2x=55

We move all terms to the left:

1/2x+2x-(55)=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-55=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-110x+1=0

a = 4; b = -110; c = +1;
Δ = b2-4ac
Δ = -1102-4·4·1
Δ = 12084
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:

$\sqrt{\Delta}=\sqrt{12084}=\sqrt{4*3021}=\sqrt{4}*\sqrt{3021}=2\sqrt{3021}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-2\sqrt{3021}}{2*4}=\frac{110-2\sqrt{3021}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+2\sqrt{3021}}{2*4}=\frac{110+2\sqrt{3021}}{8}
$