6x+1=5/x

Solution for 6x+1=5/x equation:

6x+1=5/x

We move all terms to the left:

6x+1-(5/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

6x-(+5/x)+1=0

We get rid of parentheses

6x-5/x+1=0

We multiply all the terms by the denominator


6x*x+1*x-5=0

We add all the numbers together, and all the variables

x+6x*x-5=0

Wy multiply elements

6x^2+x-5=0

a = 6; b = 1; c = -5;
Δ = b2-4ac
Δ = 12-4·6·(-5)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-11}{2*6}=\frac{-12}{12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+11}{2*6}=\frac{10}{12}
=5/6
$