5/3x+1/6x=48/9

Solution for 5/3x+1/6x=48/9 equation:

5/3x+1/6x=48/9

We move all terms to the left:

5/3x+1/6x-(48/9)=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+1/6x-(+48/9)=0

We get rid of parentheses

5/3x+1/6x-48/9=0

We calculate fractions


(-5184x^2)/1458x^2+2430x/1458x^2+243x/1458x^2=0

We multiply all the terms by the denominator


(-5184x^2)+2430x+243x=0

We add all the numbers together, and all the variables

(-5184x^2)+2673x=0

We get rid of parentheses

-5184x^2+2673x=0

a = -5184; b = 2673; c = 0;
Δ = b2-4ac
Δ = 26732-4·(-5184)·0
Δ = 7144929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7144929}=2673$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2673)-2673}{2*-5184}=\frac{-5346}{-10368}
=33/64
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2673)+2673}{2*-5184}=\frac{0}{-10368}
=0
$