3x-6=45/x

Solution for 3x-6=45/x equation:

3x-6=45/x

We move all terms to the left:

3x-6-(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

3x-(+45/x)-6=0

We get rid of parentheses

3x-45/x-6=0

We multiply all the terms by the denominator


3x*x-6*x-45=0

We add all the numbers together, and all the variables

-6x+3x*x-45=0

Wy multiply elements

3x^2-6x-45=0

a = 3; b = -6; c = -45;
Δ = b2-4ac
Δ = -62-4·3·(-45)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-24}{2*3}=\frac{-18}{6}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+24}{2*3}=\frac{30}{6}
=5
$