5/3x+5/6x=50/9

Solution for 5/3x+5/6x=50/9 equation:

5/3x+5/6x=50/9

We move all terms to the left:

5/3x+5/6x-(50/9)=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

5/3x+5/6x-(+50/9)=0

We get rid of parentheses

5/3x+5/6x-50/9=0

We calculate fractions


(-5400x^2)/1458x^2+2430x/1458x^2+1215x/1458x^2=0

We multiply all the terms by the denominator


(-5400x^2)+2430x+1215x=0

We add all the numbers together, and all the variables

(-5400x^2)+3645x=0

We get rid of parentheses

-5400x^2+3645x=0

a = -5400; b = 3645; c = 0;
Δ = b2-4ac
Δ = 36452-4·(-5400)·0
Δ = 13286025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13286025}=3645$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3645)-3645}{2*-5400}=\frac{-7290}{-10800}
=27/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3645)+3645}{2*-5400}=\frac{0}{-10800}
=0
$