6x+5=34/x

Solution for 6x+5=34/x equation:

6x+5=34/x

We move all terms to the left:

6x+5-(34/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-(+34/x)+5=0

We get rid of parentheses

6x-34/x+5=0

We multiply all the terms by the denominator


6x*x+5*x-34=0

We add all the numbers together, and all the variables

5x+6x*x-34=0

Wy multiply elements

6x^2+5x-34=0

a = 6; b = 5; c = -34;
Δ = b2-4ac
Δ = 52-4·6·(-34)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-29}{2*6}=\frac{-34}{12}
=-2+5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+29}{2*6}=\frac{24}{12}
=2
$