x+3/2x+1=-2

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

x+3/2x+1=-2

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+3/2x+3=0

We multiply all the terms by the denominator


x*2x+3*2x+3=0

Wy multiply elements

2x^2+6x+3=0

a = 2; b = 6; c = +3;
Δ = b2-4ac
Δ = 62-4·2·3
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{3}}{2*2}=\frac{-6-2\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{3}}{2*2}=\frac{-6+2\sqrt{3}}{4}
$