1/3X+1/6y=3

Solution for 1/3X+1/6y=3 equation:

1/3X+1/6X=3

We move all terms to the left:

1/3X+1/6X-(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


We calculate fractions


6X/18X^2+3X/18X^2-3=0

We multiply all the terms by the denominator


6X+3X-3*18X^2=0

We add all the numbers together, and all the variables

9X-3*18X^2=0

Wy multiply elements

-54X^2+9X=0

a = -54; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-54)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-54}=\frac{-18}{-108}
=1/6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-54}=\frac{0}{-108}
=0
$