w(10w+1)=9

Solution for w(10w+1)=9 equation:

w(10w+1)=9

We move all terms to the left:

w(10w+1)-(9)=0

We multiply parentheses

10w^2+w-9=0

a = 10; b = 1; c = -9;
Δ = b2-4ac
Δ = 12-4·10·(-9)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-19}{2*10}=\frac{-20}{20}
=-1
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+19}{2*10}=\frac{18}{20}
=9/10
$