36/x=(20*x+1)/9

Solution for 36/x=(20*x+1)/9 equation:

36/x=(20x+1)/9

We move all terms to the left:

36/x-((20x+1)/9)=0


Domain of the equation: x!=0

x∈R


We calculate fractions


()/9x^2+(-((20x+1)*x)/9x^2=0

We multiply all the terms by the denominator


(-((20x+1)*x)+()=0


We calculate terms in parentheses: +(-((20x+1)*x)+(), so:

-((20x+1)*x)+(

We add all the numbers together, and all the variables

-((20x+1)*x)


We calculate terms in parentheses: -((20x+1)*x), so:

(20x+1)*x

We multiply parentheses

20x^2+x

Back to the equation:

-(20x^2+x)


We get rid of parentheses

-20x^2-x

We add all the numbers together, and all the variables

-20x^2-1x

Back to the equation:

+(-20x^2-1x)


We get rid of parentheses

-20x^2-1x=0

a = -20; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-20)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-20}=\frac{0}{-40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-20}=\frac{2}{-40}
=-1/20
$