X-6/x+9=4/x-6

Solution for X-6/x+9=4/x-6 equation:

X-6/X+9=4/X-6

We move all terms to the left:

X-6/X+9-(4/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-6/X-4/X+6+9=0

We multiply all the terms by the denominator


X*X+6*X+9*X-6-4=0

We add all the numbers together, and all the variables

15X+X*X-10=0

Wy multiply elements

X^2+15X-10=0

a = 1; b = 15; c = -10;
Δ = b2-4ac
Δ = 152-4·1·(-10)
Δ = 265
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{-(15)-\sqrt{265}}{2*1}=\frac{-15-\sqrt{265}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{265}}{2*1}=\frac{-15+\sqrt{265}}{2}
$