100u=-5u^2

Solution for 100u=-5u^2 equation:

100u=-5u^2

We move all terms to the left:

100u-(-5u^2)=0

We get rid of parentheses

5u^2+100u=0

a = 5; b = 100; c = 0;
Δ = b2-4ac
Δ = 1002-4·5·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100}{2*5}=\frac{-200}{10}
=-20
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100}{2*5}=\frac{0}{10}
=0
$