5=60x(1/x)

Solution for 5=60x(1/x) equation:

5=60x(1/x)

We move all terms to the left:

5-(60x(1/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

-(60x(+1/x))+5=0

We multiply all the terms by the denominator


-(60x(+1+5*x))=0


We calculate terms in parentheses: -(60x(+1+5*x)), so:

60x(+1+5*x)

We add all the numbers together, and all the variables

60x(5x+1)

We multiply parentheses

300x^2+60x

Back to the equation:

-(300x^2+60x)


We get rid of parentheses

-300x^2-60x=0

a = -300; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·(-300)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*-300}=\frac{0}{-600}
=0$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*-300}=\frac{120}{-600}
=-1/5$