5-2/3x=1/9x+19

Solution for 5-2/3x=1/9x+19 equation:

5-2/3x=1/9x+19

We move all terms to the left:

5-2/3x-(1/9x+19)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x+19)!=0

x∈R


We get rid of parentheses

-2/3x-1/9x-19+5=0

We calculate fractions


(-18x)/27x^2+(-3x)/27x^2-19+5=0

We add all the numbers together, and all the variables

(-18x)/27x^2+(-3x)/27x^2-14=0

We multiply all the terms by the denominator


(-18x)+(-3x)-14*27x^2=0

Wy multiply elements

-378x^2+(-18x)+(-3x)=0

We get rid of parentheses

-378x^2-18x-3x=0

We add all the numbers together, and all the variables

-378x^2-21x=0

a = -378; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·(-378)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*-378}=\frac{0}{-756}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*-378}=\frac{42}{-756}
=-1/18
$