3/x+1=2x

Solution for 3/x+1=2x equation:

3/x+1=2x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-2x+3/x+1=0

We multiply all the terms by the denominator


-2x*x+1*x+3=0

We add all the numbers together, and all the variables

x-2x*x+3=0

Wy multiply elements

-2x^2+x+3=0

a = -2; b = 1; c = +3;
Δ = b2-4ac
Δ = 12-4·(-2)·3
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5}{2*-2}=\frac{4}{-4}
=-1
$