3/2x+5=1/9x

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

3/2x+5=1/9x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


27x+(-2x)+5*18x^2=0

Wy multiply elements

90x^2+27x+(-2x)=0

We get rid of parentheses

90x^2+27x-2x=0

We add all the numbers together, and all the variables

90x^2+25x=0

a = 90; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·90·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*90}=\frac{-50}{180}
=-5/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*90}=\frac{0}{180}
=0
$