1/6x+2/3x=5/9

Solution for 1/6x+2/3x=5/9 equation:

1/6x+2/3x=5/9

We move all terms to the left:

1/6x+2/3x-(5/9)=0


Domain of the equation: 6x!=0

x!=0/6

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

1/6x+2/3x-(+5/9)=0

We get rid of parentheses

1/6x+2/3x-5/9=0

We calculate fractions


(-270x^2)/1458x^2+243x/1458x^2+972x/1458x^2=0

We multiply all the terms by the denominator


(-270x^2)+243x+972x=0

We add all the numbers together, and all the variables

(-270x^2)+1215x=0

We get rid of parentheses

-270x^2+1215x=0

a = -270; b = 1215; c = 0;
Δ = b2-4ac
Δ = 12152-4·(-270)·0
Δ = 1476225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1476225}=1215$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1215)-1215}{2*-270}=\frac{-2430}{-540}
=4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1215)+1215}{2*-270}=\frac{0}{-540}
=0
$