6x+5=6/x

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

6x+5=6/x

We move all terms to the left:

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

We get rid of parentheses

6x-6/x+5=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

5x+6x*x-6=0

Wy multiply elements

6x^2+5x-6=0

a = 6; b = 5; c = -6;
Δ = b2-4ac
Δ = 52-4·6·(-6)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-13}{2*6}=\frac{-18}{12}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+13}{2*6}=\frac{8}{12}
=2/3
$