1/2x+1/3x=7/9

Solution for 1/2x+1/3x=7/9 equation:

1/2x+1/3x=7/9

We move all terms to the left:

1/2x+1/3x-(7/9)=0


Domain of the equation: 2x!=0

x!=0/2

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

1/2x+1/3x-(+7/9)=0

We get rid of parentheses

1/2x+1/3x-7/9=0

We calculate fractions


(-126x^2)/486x^2+243x/486x^2+162x/486x^2=0

We multiply all the terms by the denominator


(-126x^2)+243x+162x=0

We add all the numbers together, and all the variables

(-126x^2)+405x=0

We get rid of parentheses

-126x^2+405x=0

a = -126; b = 405; c = 0;
Δ = b2-4ac
Δ = 4052-4·(-126)·0
Δ = 164025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{164025}=405$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(405)-405}{2*-126}=\frac{-810}{-252}
=3+3/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(405)+405}{2*-126}=\frac{0}{-252}
=0
$