2x+18/x=13

Solution for 2x+18/x=13 equation:

2x+18/x=13

We move all terms to the left:

2x+18/x-(13)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


2x*x-13*x+18=0

We add all the numbers together, and all the variables

-13x+2x*x+18=0

Wy multiply elements

2x^2-13x+18=0

a = 2; b = -13; c = +18;
Δ = b2-4ac
Δ = -132-4·2·18
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-5}{2*2}=\frac{8}{4}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+5}{2*2}=\frac{18}{4}
=4+1/2
$