3/2x+1/x+1=0

Solution for 3/2x+1/x+1=0 equation:

3/2x+1/x+1=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


3x/2x^2+2x/2x^2+1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

5x+1*2x^2=0

Wy multiply elements

2x^2+5x=0

a = 2; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·2·0
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{-(5)-5}{2*2}=\frac{-10}{4}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*2}=\frac{0}{4}
=0
$