3/2x+2/3x=13/6

Solution for 3/2x+2/3x=13/6 equation:

3/2x+2/3x=13/6

We move all terms to the left:

3/2x+2/3x-(13/6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3/2x+2/3x-(+13/6)=0

We get rid of parentheses

3/2x+2/3x-13/6=0

We calculate fractions


(-234x^2)/216x^2+324x/216x^2+144x/216x^2=0

We multiply all the terms by the denominator


(-234x^2)+324x+144x=0

We add all the numbers together, and all the variables

(-234x^2)+468x=0

We get rid of parentheses

-234x^2+468x=0

a = -234; b = 468; c = 0;
Δ = b2-4ac
Δ = 4682-4·(-234)·0
Δ = 219024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{219024}=468$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(468)-468}{2*-234}=\frac{-936}{-468}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(468)+468}{2*-234}=\frac{0}{-468}
=0
$