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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


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

We calculate fractions


108x^2/72x^2+24x/72x^2+60x/72x^2-3=0

We multiply all the terms by the denominator


108x^2+24x+60x-3*72x^2=0

We add all the numbers together, and all the variables

108x^2+84x-3*72x^2=0

Wy multiply elements

108x^2-216x^2+84x=0

We add all the numbers together, and all the variables

-108x^2+84x=0

a = -108; b = 84; c = 0;
Δ = b2-4ac
Δ = 842-4·(-108)·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-84}{2*-108}=\frac{-168}{-216}
=7/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+84}{2*-108}=\frac{0}{-216}
=0
$