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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-2268x^2)/216x^2+81x/216x^2+24x/216x^2+81x/216x^2=0

We multiply all the terms by the denominator


(-2268x^2)+81x+24x+81x=0

We add all the numbers together, and all the variables

(-2268x^2)+186x=0

We get rid of parentheses

-2268x^2+186x=0

a = -2268; b = 186; c = 0;
Δ = b2-4ac
Δ = 1862-4·(-2268)·0
Δ = 34596
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{34596}=186$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(186)-186}{2*-2268}=\frac{-372}{-4536}
=31/378
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(186)+186}{2*-2268}=\frac{0}{-4536}
=0
$