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r(18+9r)=7
We move all terms to the left:
r(18+9r)-(7)=0
We add all the numbers together, and all the variables
r(9r+18)-7=0
We multiply parentheses
9r^2+18r-7=0
a = 9; b = 18; c = -7;
Δ = b2-4ac
Δ = 182-4·9·(-7)
Δ = 576
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{576}=24$$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-24}{2*9}=\frac{-42}{18} =-2+1/3 $$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+24}{2*9}=\frac{6}{18} =1/3 $
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