4x+1/x+2=-3

Solution for 4x+1/x+2=-3 equation:

4x+1/x+2=-3

We move all terms to the left:

4x+1/x+2-(-3)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4x+1/x+5=0

We multiply all the terms by the denominator


4x*x+5*x+1=0

We add all the numbers together, and all the variables

5x+4x*x+1=0

Wy multiply elements

4x^2+5x+1=0

a = 4; b = 5; c = +1;
Δ = b2-4ac
Δ = 52-4·4·1
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3}{2*4}=\frac{-8}{8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3}{2*4}=\frac{-2}{8}
=-1/4
$