0=r(10r-199)

Solution for 0=r(10r-199) equation:

0=r(10r-199)

We move all terms to the left:

0-(r(10r-199))=0

We add all the numbers together, and all the variables

-(r(10r-199))=0


We calculate terms in parentheses: -(r(10r-199)), so:

r(10r-199)

We multiply parentheses

10r^2-199r

Back to the equation:

-(10r^2-199r)


We get rid of parentheses

-10r^2+199r=0

a = -10; b = 199; c = 0;
Δ = b2-4ac
Δ = 1992-4·(-10)·0
Δ = 39601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{39601}=199$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(199)-199}{2*-10}=\frac{-398}{-20}
=19+9/10
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(199)+199}{2*-10}=\frac{0}{-20}
=0
$