2x+1x/2x=50

Solution for 2x+1x/2x=50 equation:

2x+1x/2x=50

We move all terms to the left:

2x+1x/2x-(50)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


2x*2x+1x-50*2x=0

We add all the numbers together, and all the variables

x+2x*2x-50*2x=0

Wy multiply elements

4x^2+x-100x=0

We add all the numbers together, and all the variables

4x^2-99x=0

a = 4; b = -99; c = 0;
Δ = b2-4ac
Δ = -992-4·4·0
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-99}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+99}{2*4}=\frac{198}{8}
=24+3/4
$