2x+19=186/x

Solution for 2x+19=186/x equation:

2x+19=186/x

We move all terms to the left:

2x+19-(186/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

2x-(+186/x)+19=0

We get rid of parentheses

2x-186/x+19=0

We multiply all the terms by the denominator


2x*x+19*x-186=0

We add all the numbers together, and all the variables

19x+2x*x-186=0

Wy multiply elements

2x^2+19x-186=0

a = 2; b = 19; c = -186;
Δ = b2-4ac
Δ = 192-4·2·(-186)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-43}{2*2}=\frac{-62}{4}
=-15+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+43}{2*2}=\frac{24}{4}
=6
$