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-4n(2n+7)=20
We move all terms to the left:
-4n(2n+7)-(20)=0
We multiply parentheses
-8n^2-28n-20=0
a = -8; b = -28; c = -20;
Δ = b2-4ac
Δ = -282-4·(-8)·(-20)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{144}=12$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-12}{2*-8}=\frac{16}{-16} =-1 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+12}{2*-8}=\frac{40}{-16} =-2+1/2 $
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