x+3/x-2=6

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

x+3/x-2=6

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+3/x-8=0

We multiply all the terms by the denominator


x*x-8*x+3=0

We add all the numbers together, and all the variables

-8x+x*x+3=0

Wy multiply elements

x^2-8x+3=0

a = 1; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·1·3
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{13}}{2*1}=\frac{8-2\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{13}}{2*1}=\frac{8+2\sqrt{13}}{2}
$