5x+(2/x)=-11

Solution for 5x+(2/x)=-11 equation:

5x+(2/x)=-11

We move all terms to the left:

5x+(2/x)-(-11)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x+(+2/x)-(-11)=0

We add all the numbers together, and all the variables

5x+(+2/x)+11=0

We get rid of parentheses

5x+2/x+11=0

We multiply all the terms by the denominator


5x*x+11*x+2=0

We add all the numbers together, and all the variables

11x+5x*x+2=0

Wy multiply elements

5x^2+11x+2=0

a = 5; b = 11; c = +2;
Δ = b2-4ac
Δ = 112-4·5·2
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-9}{2*5}=\frac{-20}{10}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+9}{2*5}=\frac{-2}{10}
=-1/5
$