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1/3r+3r=30
We move all terms to the left:
1/3r+3r-(30)=0
Domain of the equation: 3r!=0We add all the numbers together, and all the variables
r!=0/3
r!=0
r∈R
3r+1/3r-30=0
We multiply all the terms by the denominator
3r*3r-30*3r+1=0
Wy multiply elements
9r^2-90r+1=0
a = 9; b = -90; c = +1;
Δ = b2-4ac
Δ = -902-4·9·1
Δ = 8064
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}$$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8064}=\sqrt{576*14}=\sqrt{576}*\sqrt{14}=24\sqrt{14}$$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-24\sqrt{14}}{2*9}=\frac{90-24\sqrt{14}}{18} $$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+24\sqrt{14}}{2*9}=\frac{90+24\sqrt{14}}{18} $
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