200=(500/b)*b

Solution for 200=(500/b)*b equation:

200=(500/b)*b

We move all terms to the left:

200-((500/b)*b)=0


Domain of the equation: b)*b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

-((+500/b)*b)+200=0

We multiply all the terms by the denominator


-((+500+200*b)*b)=0


We calculate terms in parentheses: -((+500+200*b)*b), so:

(+500+200*b)*b

We add all the numbers together, and all the variables

(200b+500)*b

We multiply parentheses

200b^2+500b

Back to the equation:

-(200b^2+500b)


We get rid of parentheses

-200b^2-500b=0

a = -200; b = -500; c = 0;
Δ = b2-4ac
Δ = -5002-4·(-200)·0
Δ = 250000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{250000}=500$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-500}{2*-200}=\frac{0}{-400}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+500}{2*-200}=\frac{1000}{-400}
=-2+1/2
$