(11x-33)/(x-3)=x

Solution for (11x-33)/(x-3)=x equation:

(11x-33)/(x-3)=x

We move all terms to the left:

(11x-33)/(x-3)-(x)=0


Domain of the equation: (x-3)!=0

We move all terms containing x to the left, all other terms to the right

x!=3

x∈R


We add all the numbers together, and all the variables

-1x+(11x-33)/(x-3)=0

We multiply all the terms by the denominator


-1x*(x-3)+(11x-33)=0

We multiply parentheses

-x^2+3x+(11x-33)=0

We get rid of parentheses

-x^2+3x+11x-33=0

We add all the numbers together, and all the variables

-1x^2+14x-33=0

a = -1; b = 14; c = -33;
Δ = b2-4ac
Δ = 142-4·(-1)·(-33)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-8}{2*-1}=\frac{-22}{-2}
=+11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+8}{2*-1}=\frac{-6}{-2}
=+3
$