36/x-5=17/2x

Solution for 36/x-5=17/2x equation:

36/x-5=17/2x

We move all terms to the left:

36/x-5-(17/2x)=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

36/x-(+17/2x)-5=0

We get rid of parentheses

36/x-17/2x-5=0

We calculate fractions


72x/2x^2+(-17x)/2x^2-5=0

We multiply all the terms by the denominator


72x+(-17x)-5*2x^2=0

Wy multiply elements

-10x^2+72x+(-17x)=0

We get rid of parentheses

-10x^2+72x-17x=0

We add all the numbers together, and all the variables

-10x^2+55x=0

a = -10; b = 55; c = 0;
Δ = b2-4ac
Δ = 552-4·(-10)·0
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-55}{2*-10}=\frac{-110}{-20}
=5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+55}{2*-10}=\frac{0}{-20}
=0
$