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(8n+8)(9n)=90
We move all terms to the left:
(8n+8)(9n)-(90)=0
We multiply parentheses
72n^2+72n-90=0
a = 72; b = 72; c = -90;
Δ = b2-4ac
Δ = 722-4·72·(-90)
Δ = 31104
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{31104}=\sqrt{5184*6}=\sqrt{5184}*\sqrt{6}=72\sqrt{6}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-72\sqrt{6}}{2*72}=\frac{-72-72\sqrt{6}}{144} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+72\sqrt{6}}{2*72}=\frac{-72+72\sqrt{6}}{144} $
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