d(10d-9)+1=0

Solution for d(10d-9)+1=0 equation:

d(10d-9)+1=0

We multiply parentheses

10d^2-9d+1=0

a = 10; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·10·1
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{41}}{2*10}=\frac{9-\sqrt{41}}{20}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{41}}{2*10}=\frac{9+\sqrt{41}}{20}
$