9+x+3/x=3

Solution for 9+x+3/x=3 equation:

9+x+3/x=3

We move all terms to the left:

9+x+3/x-(3)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+3/x+6=0

We multiply all the terms by the denominator


x*x+6*x+3=0

We add all the numbers together, and all the variables

6x+x*x+3=0

Wy multiply elements

x^2+6x+3=0

a = 1; b = 6; c = +3;
Δ = b2-4ac
Δ = 62-4·1·3
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{6}}{2*1}=\frac{-6-2\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{6}}{2*1}=\frac{-6+2\sqrt{6}}{2}
$