4/x-2=x-6/x+3

Solution for 4/x-2=x-6/x+3 equation:

4/x-2=x-6/x+3

We move all terms to the left:

4/x-2-(x-6/x+3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+3)!=0

x∈R


We get rid of parentheses

4/x-x+6/x-3-2=0

We multiply all the terms by the denominator


-x*x-3*x-2*x+4+6=0

We add all the numbers together, and all the variables

-5x-x*x+10=0

Wy multiply elements

-1x^2-5x+10=0

a = -1; b = -5; c = +10;
Δ = b2-4ac
Δ = -52-4·(-1)·10
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{-(-5)-\sqrt{65}}{2*-1}=\frac{5-\sqrt{65}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{65}}{2*-1}=\frac{5+\sqrt{65}}{-2}
$