3+4x=45/x

Solution for 3+4x=45/x equation:

3+4x=45/x

We move all terms to the left:

3+4x-(45/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

4x-(+45/x)+3=0

We get rid of parentheses

4x-45/x+3=0

We multiply all the terms by the denominator


4x*x+3*x-45=0

We add all the numbers together, and all the variables

3x+4x*x-45=0

Wy multiply elements

4x^2+3x-45=0

a = 4; b = 3; c = -45;
Δ = b2-4ac
Δ = 32-4·4·(-45)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-27}{2*4}=\frac{-30}{8}
=-3+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+27}{2*4}=\frac{24}{8}
=3
$