6/x=45+3/2x

Solution for 6/x=45+3/2x equation:

6/x=45+3/2x

We move all terms to the left:

6/x-(45+3/2x)=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

6/x-(3/2x+45)=0

We get rid of parentheses

6/x-3/2x-45=0

We calculate fractions


12x/2x^2+(-3x)/2x^2-45=0

We multiply all the terms by the denominator


12x+(-3x)-45*2x^2=0

Wy multiply elements

-90x^2+12x+(-3x)=0

We get rid of parentheses

-90x^2+12x-3x=0

We add all the numbers together, and all the variables

-90x^2+9x=0

a = -90; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-90)·0
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{-(9)-9}{2*-90}=\frac{-18}{-180}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-90}=\frac{0}{-180}
=0
$