u(9u+1)=0

Solution for u(9u+1)=0 equation:

u(9u+1)=0

We multiply parentheses

9u^2+u=0

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

$\sqrt{\Delta}=\sqrt{1}=1$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*9}=\frac{-2}{18}
=-1/9
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*9}=\frac{0}{18}
=0
$