9r^2=55-18r

Solution for 9r^2=55-18r equation:

9r^2=55-18r

We move all terms to the left:

9r^2-(55-18r)=0

We add all the numbers together, and all the variables

9r^2-(-18r+55)=0

We get rid of parentheses

9r^2+18r-55=0

a = 9; b = 18; c = -55;
Δ = b2-4ac
Δ = 182-4·9·(-55)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-48}{2*9}=\frac{-66}{18}
=-3+2/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+48}{2*9}=\frac{30}{18}
=1+2/3
$