4x+(4/x)+13=0

Solution for 4x+(4/x)+13=0 equation:

4x+(4/x)+13=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x+(+4/x)+13=0

We get rid of parentheses

4x+4/x+13=0

We multiply all the terms by the denominator


4x*x+13*x+4=0

We add all the numbers together, and all the variables

13x+4x*x+4=0

Wy multiply elements

4x^2+13x+4=0

a = 4; b = 13; c = +4;
Δ = b2-4ac
Δ = 132-4·4·4
Δ = 105
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{105}}{2*4}=\frac{-13-\sqrt{105}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{105}}{2*4}=\frac{-13+\sqrt{105}}{8}
$