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!=0

x∈R


We add all the numbers together, and all the variables

10x-33/x-3=0

We multiply all the terms by the denominator


10x*x-3*x-33=0

We add all the numbers together, and all the variables

-3x+10x*x-33=0

Wy multiply elements

10x^2-3x-33=0

a = 10; b = -3; c = -33;
Δ = b2-4ac
Δ = -32-4·10·(-33)
Δ = 1329
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{-(-3)-\sqrt{1329}}{2*10}=\frac{3-\sqrt{1329}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{1329}}{2*10}=\frac{3+\sqrt{1329}}{20}
$