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5(b-2)b=20
We move all terms to the left:
5(b-2)b-(20)=0
We multiply parentheses
5b^2-10b-20=0
a = 5; b = -10; c = -20;
Δ = b2-4ac
Δ = -102-4·5·(-20)
Δ = 500
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}$$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{5}}{2*5}=\frac{10-10\sqrt{5}}{10} $$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{5}}{2*5}=\frac{10+10\sqrt{5}}{10} $
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