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

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

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

We move all terms to the left:

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


We add all the numbers together, and all the variables

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

We calculate fractions


6x/18x^2+15x/18x^2+3=0

We multiply all the terms by the denominator


6x+15x+3*18x^2=0

We add all the numbers together, and all the variables

21x+3*18x^2=0

Wy multiply elements

54x^2+21x=0

a = 54; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·54·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*54}=\frac{-42}{108}
=-7/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*54}=\frac{0}{108}
=0
$