r(9r-r)=360

Solution for r(9r-r)=360 equation:

r(9r-r)=360

We move all terms to the left:

r(9r-r)-(360)=0

We add all the numbers together, and all the variables

r(+8r)-360=0

We multiply parentheses

8r^2-360=0

a = 8; b = 0; c = -360;
Δ = b2-4ac
Δ = 02-4·8·(-360)
Δ = 11520
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{11520}=\sqrt{2304*5}=\sqrt{2304}*\sqrt{5}=48\sqrt{5}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{5}}{2*8}=\frac{0-48\sqrt{5}}{16}
=-\frac{48\sqrt{5}}{16}
=-3\sqrt{5}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{5}}{2*8}=\frac{0+48\sqrt{5}}{16}
=\frac{48\sqrt{5}}{16}
=3\sqrt{5}
$