11x-33/x-2=x

Solution for 11x-33/x-2=x equation:

11x-33/x-2=x

We move all terms to the left:

11x-33/x-2-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

10x-33/x-2=0

We multiply all the terms by the denominator


10x*x-2*x-33=0

We add all the numbers together, and all the variables

-2x+10x*x-33=0

Wy multiply elements

10x^2-2x-33=0

a = 10; b = -2; c = -33;
Δ = b2-4ac
Δ = -22-4·10·(-33)
Δ = 1324
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:

$\sqrt{\Delta}=\sqrt{1324}=\sqrt{4*331}=\sqrt{4}*\sqrt{331}=2\sqrt{331}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{331}}{2*10}=\frac{2-2\sqrt{331}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{331}}{2*10}=\frac{2+2\sqrt{331}}{20}
$