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n(4n+4)+4=28
We move all terms to the left:
n(4n+4)+4-(28)=0
We add all the numbers together, and all the variables
n(4n+4)-24=0
We multiply parentheses
4n^2+4n-24=0
a = 4; b = 4; c = -24;
Δ = b2-4ac
Δ = 42-4·4·(-24)
Δ = 400
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{400}=20$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-20}{2*4}=\frac{-24}{8} =-3 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+20}{2*4}=\frac{16}{8} =2 $
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