x-9/x+6=0

Solution for x-9/x+6=0 equation:

x-9/x+6=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x+6*x-9=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}
$