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2*3.14r*r+2*3.14r*10=297
We move all terms to the left:
2*3.14r*r+2*3.14r*10-(297)=0
Wy multiply elements
6r^2+60r-297=0
a = 6; b = 60; c = -297;
Δ = b2-4ac
Δ = 602-4·6·(-297)
Δ = 10728
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}$$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10728}=\sqrt{36*298}=\sqrt{36}*\sqrt{298}=6\sqrt{298}$$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-6\sqrt{298}}{2*6}=\frac{-60-6\sqrt{298}}{12} $$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+6\sqrt{298}}{2*6}=\frac{-60+6\sqrt{298}}{12} $
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