-400r=100r^2

Solution for -400r=100r^2 equation:

-400r=100r^2

We move all terms to the left:

-400r-(100r^2)=0

determiningTheFunctionDomain
-100r^2-400r=0

a = -100; b = -400; c = 0;
Δ = b2-4ac
Δ = -4002-4·(-100)·0
Δ = 160000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{160000}=400$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-400}{2*-100}=\frac{0}{-200}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+400}{2*-100}=\frac{800}{-200}
=-4
$