x+3=-3/x-2

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

x+3=-3/x-2

We move all terms to the left:

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


Domain of the equation: x-2)!=0

x∈R


We get rid of parentheses

x+3/x+2+3=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

5x+x*x+3=0

Wy multiply elements

x^2+5x+3=0

a = 1; b = 5; c = +3;
Δ = b2-4ac
Δ = 52-4·1·3
Δ = 13
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{-(5)-\sqrt{13}}{2*1}=\frac{-5-\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{13}}{2*1}=\frac{-5+\sqrt{13}}{2}
$