180/x+3/2=360+3x/2x

Solution for 180/x+3/2=360+3x/2x equation:

180/x+3/2=360+3x/2x

We move all terms to the left:

180/x+3/2-(360+3x/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

180/x-(3x/2x+360)+3/2=0

We get rid of parentheses

180/x-3x/2x-360+3/2=0

We calculate fractions


(-3x^2)/8x^2+1440x/8x^2+3x/8x^2-360=0

We multiply all the terms by the denominator


(-3x^2)+1440x+3x-360*8x^2=0

We add all the numbers together, and all the variables

(-3x^2)+1443x-360*8x^2=0

Wy multiply elements

(-3x^2)-2880x^2+1443x=0

We get rid of parentheses

-3x^2-2880x^2+1443x=0

We add all the numbers together, and all the variables

-2883x^2+1443x=0

a = -2883; b = 1443; c = 0;
Δ = b2-4ac
Δ = 14432-4·(-2883)·0
Δ = 2082249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2082249}=1443$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1443)-1443}{2*-2883}=\frac{-2886}{-5766}
=481/961
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1443)+1443}{2*-2883}=\frac{0}{-5766}
=0
$