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4(2n^2-7)=44
We move all terms to the left:
4(2n^2-7)-(44)=0
We multiply parentheses
8n^2-28-44=0
We add all the numbers together, and all the variables
8n^2-72=0
a = 8; b = 0; c = -72;
Δ = b2-4ac
Δ = 02-4·8·(-72)
Δ = 2304
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{2304}=48$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48}{2*8}=\frac{-48}{16} =-3 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48}{2*8}=\frac{48}{16} =3 $
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