X+3/2x+3=-1

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

X+3/2X+3=-1

We move all terms to the left:

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

We multiply all the terms by the denominator


X*2X+4*2X+3=0

Wy multiply elements

2X^2+8X+3=0

a = 2; b = 8; c = +3;
Δ = b2-4ac
Δ = 82-4·2·3
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{10}}{2*2}=\frac{-8-2\sqrt{10}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{10}}{2*2}=\frac{-8+2\sqrt{10}}{4}
$