r=r^2+3r+9r+27

Solution for r=r^2+3r+9r+27 equation:

r=r^2+3r+9r+27

We move all terms to the left:

r-(r^2+3r+9r+27)=0

We get rid of parentheses

-r^2+r-3r-9r-27=0

We add all the numbers together, and all the variables

-1r^2-11r-27=0

a = -1; b = -11; c = -27;
Δ = b2-4ac
Δ = -112-4·(-1)·(-27)
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{13}}{2*-1}=\frac{11-\sqrt{13}}{-2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{13}}{2*-1}=\frac{11+\sqrt{13}}{-2}
$