x=9x^2-2x-1

Solution for x=9x^2-2x-1 equation:

x=9x^2-2x-1

We move all terms to the left:

x-(9x^2-2x-1)=0

We get rid of parentheses

-9x^2+x+2x+1=0

We add all the numbers together, and all the variables

-9x^2+3x+1=0

a = -9; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·(-9)·1
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{5}}{2*-9}=\frac{-3-3\sqrt{5}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{5}}{2*-9}=\frac{-3+3\sqrt{5}}{-18}
$