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100-b2=80
We move all terms to the left:
100-b2-(80)=0
We add all the numbers together, and all the variables
-1b^2+20=0
a = -1; b = 0; c = +20;
Δ = b2-4ac
Δ = 02-4·(-1)·20
Δ = 80
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*-1}=\frac{0-4\sqrt{5}}{-2} =-\frac{4\sqrt{5}}{-2} =-\frac{2\sqrt{5}}{-1} $$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*-1}=\frac{0+4\sqrt{5}}{-2} =\frac{4\sqrt{5}}{-2} =\frac{2\sqrt{5}}{-1} $
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