1+1/x=9/2x

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

1+1/x=9/2x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


2x/2x^2+(-9x)/2x^2+1=0

We multiply all the terms by the denominator


2x+(-9x)+1*2x^2=0

Wy multiply elements

2x^2+2x+(-9x)=0

We get rid of parentheses

2x^2+2x-9x=0

We add all the numbers together, and all the variables

2x^2-7x=0

a = 2; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·2·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*2}=\frac{14}{4}
=3+1/2
$