5u(2u+5)=0

Solution for 5u(2u+5)=0 equation:

5u(2u+5)=0

We multiply parentheses

10u^2+25u=0

a = 10; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·10·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*10}=\frac{-50}{20}
=-2+1/2
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*10}=\frac{0}{20}
=0
$