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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+3)!=0

x∈R


We add all the numbers together, and all the variables

3x/x-(-3/2x+6)+1=0

We get rid of parentheses

3x/x+3/2x-6+1=0

We calculate fractions


6x^2/2x^2+3x/2x^2-6+1=0

We add all the numbers together, and all the variables

6x^2/2x^2+3x/2x^2-5=0

We multiply all the terms by the denominator


6x^2+3x-5*2x^2=0

Wy multiply elements

6x^2-10x^2+3x=0

We add all the numbers together, and all the variables

-4x^2+3x=0

a = -4; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-4)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-4}=\frac{-6}{-8}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-4}=\frac{0}{-8}
=0
$