3+x=6/x-2

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

3+x=6/x-2

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

x-6/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

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