200=5v(100+2v)

Solution for 200=5v(100+2v) equation:

200=5v(100+2v)

We move all terms to the left:

200-(5v(100+2v))=0

We add all the numbers together, and all the variables

-(5v(2v+100))+200=0


We calculate terms in parentheses: -(5v(2v+100)), so:

5v(2v+100)

We multiply parentheses

10v^2+500v

Back to the equation:

-(10v^2+500v)


We get rid of parentheses

-10v^2-500v+200=0

a = -10; b = -500; c = +200;
Δ = b2-4ac
Δ = -5002-4·(-10)·200
Δ = 258000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{258000}=\sqrt{400*645}=\sqrt{400}*\sqrt{645}=20\sqrt{645}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-20\sqrt{645}}{2*-10}=\frac{500-20\sqrt{645}}{-20}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+20\sqrt{645}}{2*-10}=\frac{500+20\sqrt{645}}{-20}
$