4/3x+2/6x=50/9

Solution for 4/3x+2/6x=50/9 equation:

4/3x+2/6x=50/9

We move all terms to the left:

4/3x+2/6x-(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

4/3x+2/6x-(+50/9)=0

We get rid of parentheses

4/3x+2/6x-50/9=0

We calculate fractions


(-5400x^2)/1458x^2+1944x/1458x^2+486x/1458x^2=0

We multiply all the terms by the denominator


(-5400x^2)+1944x+486x=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

-5400x^2+2430x=0

a = -5400; b = 2430; c = 0;
Δ = b2-4ac
Δ = 24302-4·(-5400)·0
Δ = 5904900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5904900}=2430$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2430)-2430}{2*-5400}=\frac{-4860}{-10800}
=9/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2430)+2430}{2*-5400}=\frac{0}{-10800}
=0
$