x=9x^2-11x

Solution for x=9x^2-11x equation:

x=9x^2-11x

We move all terms to the left:

x-(9x^2-11x)=0

We get rid of parentheses

-9x^2+x+11x=0

We add all the numbers together, and all the variables

-9x^2+12x=0

a = -9; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-9)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-9}=\frac{-24}{-18}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-9}=\frac{0}{-18}
=0
$