90=1r(r+1)

Solution for 90=1r(r+1) equation:

90=1r(r+1)

We move all terms to the left:

90-(1r(r+1))=0


We calculate terms in parentheses: -(1r(r+1)), so:

1r(r+1)

We multiply parentheses

r^2+r

Back to the equation:

-(r^2+r)


We get rid of parentheses

-r^2-r+90=0

We add all the numbers together, and all the variables

-1r^2-1r+90=0

a = -1; b = -1; c = +90;
Δ = b2-4ac
Δ = -12-4·(-1)·90
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-19}{2*-1}=\frac{-18}{-2}
=+9
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+19}{2*-1}=\frac{20}{-2}
=-10
$