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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


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

We calculate fractions


16x/8x^2+3x/8x^2+(-x)/8x^2-3=0

We add all the numbers together, and all the variables

16x/8x^2+3x/8x^2+(-1x)/8x^2-3=0

We multiply all the terms by the denominator


16x+3x+(-1x)-3*8x^2=0

We add all the numbers together, and all the variables

19x+(-1x)-3*8x^2=0

Wy multiply elements

-24x^2+19x+(-1x)=0

We get rid of parentheses

-24x^2+19x-1x=0

We add all the numbers together, and all the variables

-24x^2+18x=0

a = -24; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-24)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-24}=\frac{-36}{-48}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-24}=\frac{0}{-48}
=0
$