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-9(n+4)=-5n(4n+36)
We move all terms to the left:
-9(n+4)-(-5n(4n+36))=0
We multiply parentheses
-9n-(-5n(4n+36))-36=0
We calculate terms in parentheses: -(-5n(4n+36)), so:We get rid of parentheses
-5n(4n+36)
We multiply parentheses
-20n^2-180n
Back to the equation:
-(-20n^2-180n)
20n^2+180n-9n-36=0
We add all the numbers together, and all the variables
20n^2+171n-36=0
a = 20; b = 171; c = -36;
Δ = b2-4ac
Δ = 1712-4·20·(-36)
Δ = 32121
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{32121}=\sqrt{9*3569}=\sqrt{9}*\sqrt{3569}=3\sqrt{3569}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(171)-3\sqrt{3569}}{2*20}=\frac{-171-3\sqrt{3569}}{40} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(171)+3\sqrt{3569}}{2*20}=\frac{-171+3\sqrt{3569}}{40} $
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