2/3x-1/9x+5=30

Solution for 2/3x-1/9x+5=30 equation:

2/3x-1/9x+5=30

We move all terms to the left:

2/3x-1/9x+5-(30)=0


Domain of the equation: 3x!=0

x!=0/3

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

2/3x-1/9x-25=0

We calculate fractions


18x/27x^2+(-3x)/27x^2-25=0

We multiply all the terms by the denominator


18x+(-3x)-25*27x^2=0

Wy multiply elements

-675x^2+18x+(-3x)=0

We get rid of parentheses

-675x^2+18x-3x=0

We add all the numbers together, and all the variables

-675x^2+15x=0

a = -675; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-675)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-675}=\frac{-30}{-1350}
=1/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-675}=\frac{0}{-1350}
=0
$