0=x+3/x-6

Solution for 0=x+3/x-6 equation:

0=x+3/x-6

We move all terms to the left:

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


Domain of the equation: x-6)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-x-3/x+6=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

6x-x*x-3=0

Wy multiply elements

-1x^2+6x-3=0

a = -1; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·(-1)·(-3)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{6}}{2*-1}=\frac{-6-2\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{6}}{2*-1}=\frac{-6+2\sqrt{6}}{-2}
$