-4/x-2=x+3

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

-4/x-2=x+3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

-4/x-x-3-2=0

We multiply all the terms by the denominator


-x*x-3*x-2*x-4=0

We add all the numbers together, and all the variables

-5x-x*x-4=0

Wy multiply elements

-1x^2-5x-4=0

a = -1; b = -5; c = -4;
Δ = b2-4ac
Δ = -52-4·(-1)·(-4)
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*-1}=\frac{2}{-2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*-1}=\frac{8}{-2}
=-4
$