2x+17/x=13

Solution for 2x+17/x=13 equation:

2x+17/x=13

We move all terms to the left:

2x+17/x-(13)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


2x*x-13*x+17=0

We add all the numbers together, and all the variables

-13x+2x*x+17=0

Wy multiply elements

2x^2-13x+17=0

a = 2; b = -13; c = +17;
Δ = b2-4ac
Δ = -132-4·2·17
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{33}}{2*2}=\frac{13-\sqrt{33}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{33}}{2*2}=\frac{13+\sqrt{33}}{4}
$