1/3x+1/2x+2/3=19/6

Solution for 1/3x+1/2x+2/3=19/6 equation:

1/3x+1/2x+2/3=19/6

We move all terms to the left:

1/3x+1/2x+2/3-(19/6)=0


Domain of the equation: 3x!=0

x!=0/3

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

1/3x+1/2x+2/3-(+19/6)=0

We get rid of parentheses

1/3x+1/2x+2/3-19/6=0

We calculate fractions


(-684x^2)/324x^2+72x/324x^2+162x/324x^2+144x/324x^2=0

We multiply all the terms by the denominator


(-684x^2)+72x+162x+144x=0

We add all the numbers together, and all the variables

(-684x^2)+378x=0

We get rid of parentheses

-684x^2+378x=0

a = -684; b = 378; c = 0;
Δ = b2-4ac
Δ = 3782-4·(-684)·0
Δ = 142884
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{142884}=378$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(378)-378}{2*-684}=\frac{-756}{-1368}
=21/38
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(378)+378}{2*-684}=\frac{0}{-1368}
=0
$