6/x-3=x+2

Solution for 6/x-3=x+2 equation:

6/x-3=x+2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

6/x-x-2-3=0

We multiply all the terms by the denominator


-x*x-2*x-3*x+6=0

We add all the numbers together, and all the variables

-5x-x*x+6=0

Wy multiply elements

-1x^2-5x+6=0

a = -1; b = -5; c = +6;
Δ = b2-4ac
Δ = -52-4·(-1)·6
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*-1}=\frac{12}{-2}
=-6
$