6x+5/x+17=0

Solution for 6x+5/x+17=0 equation:

6x+5/x+17=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


6x*x+17*x+5=0

We add all the numbers together, and all the variables

17x+6x*x+5=0

Wy multiply elements

6x^2+17x+5=0

a = 6; b = 17; c = +5;
Δ = b2-4ac
Δ = 172-4·6·5
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{-(17)-13}{2*6}=\frac{-30}{12}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+13}{2*6}=\frac{-4}{12}
=-1/3
$