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

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

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/x-3/2x-1=0

We calculate fractions


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

We multiply all the terms by the denominator


2x+(-3x)-1*2x^2=0

Wy multiply elements

-2x^2+2x+(-3x)=0

We get rid of parentheses

-2x^2+2x-3x=0

We add all the numbers together, and all the variables

-2x^2-1x=0

a = -2; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-2)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-2}=\frac{0}{-4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-2}=\frac{2}{-4}
=-1/2
$