x+4/x-3=6

Solution for x+4/x-3=6 equation:

x+4/x-3=6

We move all terms to the left:

x+4/x-3-(6)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+4/x-9=0

We multiply all the terms by the denominator


x*x-9*x+4=0

We add all the numbers together, and all the variables

-9x+x*x+4=0

Wy multiply elements

x^2-9x+4=0

a = 1; b = -9; c = +4;
Δ = b2-4ac
Δ = -92-4·1·4
Δ = 65
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{-(-9)-\sqrt{65}}{2*1}=\frac{9-\sqrt{65}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{65}}{2*1}=\frac{9+\sqrt{65}}{2}
$