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6n(n-1)+4=44
We move all terms to the left:
6n(n-1)+4-(44)=0
We add all the numbers together, and all the variables
6n(n-1)-40=0
We multiply parentheses
6n^2-6n-40=0
a = 6; b = -6; c = -40;
Δ = b2-4ac
Δ = -62-4·6·(-40)
Δ = 996
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{249}}{2*6}=\frac{6-2\sqrt{249}}{12} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{249}}{2*6}=\frac{6+2\sqrt{249}}{12} $
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