9/3=x-6/x+6

Solution for 9/3=x-6/x+6 equation:

9/3=x-6/x+6

We move all terms to the left:

9/3-(x-6/x+6)=0


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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-x+6/x-6+3=0

We multiply all the terms by the denominator


-x*x-6*x+3*x+6=0

We add all the numbers together, and all the variables

-3x-x*x+6=0

Wy multiply elements

-1x^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}
$