X+3/x-3=6/3

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

X+3/X-3=6/3

We move all terms to the left:

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


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X+3/X-3-2=0

We add all the numbers together, and all the variables

X+3/X-5=0

We multiply all the terms by the denominator


X*X-5*X+3=0

We add all the numbers together, and all the variables

-5X+X*X+3=0

Wy multiply elements

X^2-5X+3=0

a = 1; b = -5; c = +3;
Δ = b2-4ac
Δ = -52-4·1·3
Δ = 13
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{-(-5)-\sqrt{13}}{2*1}=\frac{5-\sqrt{13}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{13}}{2*1}=\frac{5+\sqrt{13}}{2}
$