u(7u+5)=0

Solution for u(7u+5)=0 equation:

u(7u+5)=0

We multiply parentheses

7u^2+5u=0

a = 7; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·7·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*7}=\frac{-10}{14}
=-5/7
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*7}=\frac{0}{14}
=0
$