X-3/x=6/x+6

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

X-3/X=6/X+6

We move all terms to the left:

X-3/X-(6/X+6)=0


Domain of the equation: X!=0

X∈R



Domain of the equation: X+6)!=0

X∈R


We get rid of parentheses

X-3/X-6/X-6=0

We multiply all the terms by the denominator


X*X-6*X-3-6=0

We add all the numbers together, and all the variables

-6X+X*X-9=0

Wy multiply elements

X^2-6X-9=0

a = 1; b = -6; c = -9;
Δ = b2-4ac
Δ = -62-4·1·(-9)
Δ = 72
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{2}}{2*1}=\frac{6-6\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{2}}{2*1}=\frac{6+6\sqrt{2}}{2}
$