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

Solution for 6/x+1-3/2=2/3x+3 equation:

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


(-27x^2)/12x^2+72x/12x^2+(-8x)/12x^2-3+1=0

We add all the numbers together, and all the variables

(-27x^2)/12x^2+72x/12x^2+(-8x)/12x^2-2=0

We multiply all the terms by the denominator


(-27x^2)+72x+(-8x)-2*12x^2=0

Wy multiply elements

(-27x^2)-24x^2+72x+(-8x)=0

We get rid of parentheses

-27x^2-24x^2+72x-8x=0

We add all the numbers together, and all the variables

-51x^2+64x=0

a = -51; b = 64; c = 0;
Δ = b2-4ac
Δ = 642-4·(-51)·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-64}{2*-51}=\frac{-128}{-102}
=1+13/51
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64}{2*-51}=\frac{0}{-102}
=0
$