X+5/5=6/x-2

Solution for X+5/5=6/x-2 equation:

X+5/5=6/X-2

We move all terms to the left:

X+5/5-(6/X-2)=0


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

X∈R


We add all the numbers together, and all the variables

X-(6/X-2)+1=0

We get rid of parentheses

X-6/X+2+1=0

We multiply all the terms by the denominator


X*X+2*X+1*X-6=0

We add all the numbers together, and all the variables

3X+X*X-6=0

Wy multiply elements

X^2+3X-6=0

a = 1; b = 3; c = -6;
Δ = b2-4ac
Δ = 32-4·1·(-6)
Δ = 33
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{-(3)-\sqrt{33}}{2*1}=\frac{-3-\sqrt{33}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{33}}{2*1}=\frac{-3+\sqrt{33}}{2}
$