9x/x+1+18/2x=21/x

Solution for 9x/x+1+18/2x=21/x equation:

9x/x+1+18/2x=21/x

We move all terms to the left:

9x/x+1+18/2x-(21/x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9x/x+18/2x-(+21/x)+1=0

We get rid of parentheses

9x/x+18/2x-21/x+1=0

We calculate fractions


(-33x)/2x^2+18x/2x^2+1=0

We multiply all the terms by the denominator


(-33x)+18x+1*2x^2=0

We add all the numbers together, and all the variables

18x+(-33x)+1*2x^2=0

Wy multiply elements

2x^2+18x+(-33x)=0

We get rid of parentheses

2x^2+18x-33x=0

We add all the numbers together, and all the variables

2x^2-15x=0

a = 2; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·2·0
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*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*2}=\frac{30}{4}
=7+1/2
$