2x+3=9/x

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

2x+3=9/x

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2x-9/x+3=0

We multiply all the terms by the denominator


2x*x+3*x-9=0

We add all the numbers together, and all the variables

3x+2x*x-9=0

Wy multiply elements

2x^2+3x-9=0

a = 2; b = 3; c = -9;
Δ = b2-4ac
Δ = 32-4·2·(-9)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*2}=\frac{-12}{4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*2}=\frac{6}{4}
=1+1/2
$