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8r^2+1=321
We move all terms to the left:
8r^2+1-(321)=0
We add all the numbers together, and all the variables
8r^2-320=0
a = 8; b = 0; c = -320;
Δ = b2-4ac
Δ = 02-4·8·(-320)
Δ = 10240
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}$$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10240}=\sqrt{1024*10}=\sqrt{1024}*\sqrt{10}=32\sqrt{10}$$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{10}}{2*8}=\frac{0-32\sqrt{10}}{16} =-\frac{32\sqrt{10}}{16} =-2\sqrt{10} $$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{10}}{2*8}=\frac{0+32\sqrt{10}}{16} =\frac{32\sqrt{10}}{16} =2\sqrt{10} $
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