4x+4/x+11=0

Solution for 4x+4/x+11=0 equation:

4x+4/x+11=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


4x*x+11*x+4=0

We add all the numbers together, and all the variables

11x+4x*x+4=0

Wy multiply elements

4x^2+11x+4=0

a = 4; b = 11; c = +4;
Δ = b2-4ac
Δ = 112-4·4·4
Δ = 57
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{-(11)-\sqrt{57}}{2*4}=\frac{-11-\sqrt{57}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{57}}{2*4}=\frac{-11+\sqrt{57}}{8}
$