u(7u-9)=0

Solution for u(7u-9)=0 equation:

u(7u-9)=0

We multiply parentheses

7u^2-9u=0

a = 7; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·7·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*7}=\frac{0}{14}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*7}=\frac{18}{14}
=1+2/7
$