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

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

^2=9D^2+2D-1

We move all terms to the left:

^2-(9D^2+2D-1)=0

We add all the numbers together, and all the variables

-(9D^2+2D-1)=0

We get rid of parentheses

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

a = -9; b = -2; c = +1;
Δ = b2-4ac
Δ = -22-4·(-9)·1
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{10}}{2*-9}=\frac{2-2\sqrt{10}}{-18}
$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{10}}{2*-9}=\frac{2+2\sqrt{10}}{-18}
$