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

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

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

We move all terms to the left:

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

We calculate fractions


324x^2/72x^2+24x/72x^2+(-60x)/72x^2-3=0

We multiply all the terms by the denominator


324x^2+24x+(-60x)-3*72x^2=0

Wy multiply elements

324x^2-216x^2+24x+(-60x)=0

We get rid of parentheses

324x^2-216x^2+24x-60x=0

We add all the numbers together, and all the variables

108x^2-36x=0

a = 108; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·108·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*108}=\frac{0}{216}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*108}=\frac{72}{216}
=1/3
$