1/2x+3/3x=5/6

Solution for 1/2x+3/3x=5/6 equation:

1/2x+3/3x=5/6

We move all terms to the left:

1/2x+3/3x-(5/6)=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

1/2x+3/3x-(+5/6)=0

We get rid of parentheses

1/2x+3/3x-5/6=0

We calculate fractions


(-90x^2)/216x^2+108x/216x^2+216x/216x^2=0

We multiply all the terms by the denominator


(-90x^2)+108x+216x=0

We add all the numbers together, and all the variables

(-90x^2)+324x=0

We get rid of parentheses

-90x^2+324x=0

a = -90; b = 324; c = 0;
Δ = b2-4ac
Δ = 3242-4·(-90)·0
Δ = 104976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{104976}=324$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(324)-324}{2*-90}=\frac{-648}{-180}
=3+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(324)+324}{2*-90}=\frac{0}{-180}
=0
$