Question

BOA NOITE, COMO EU RESOLVO ESTA EQUAÇÃO?

10n*(n+2)=800

Answer 1

10n(n+2)=800
10n^2+20n=800
10n^2+20n-800=0
delta=b^2-4ac
delta=20^2-4.10.(-800)
delta=400+32000
delta=32400
n=-b-/+ raiz de delta/2a
n=-20-180/2.10
n=200/20
n=10
n=-20+180/2.10
n=160/20
n=8

Answer 2

$10n*(n+2)=800\to \\\\10n^2+20n-800=0\\\\ a=10;\ b=20;\ c=-800\\\\\\ \Delta=b^2-4ac\to \Delta=20^2-4*10*(-800)\to \Delta=400+32000\to \\ \Delta=32400\\\\x' \neq x''\\ \\\\ x= \frac{-b\pm \sqrt{\Delta} }{2a} \to x= \frac{-20\pm \sqrt{32400} }{2*10} \to x= \frac{-20\pm 180}{20} \to \\\\\\ x'= \frac{-20+ 180}{20} \to x'= \frac{160}{20} \to x'=8\\\\\\ x''= \frac{-20- 180}{20} \to x''= \frac{-200}{20} \to x''=-10\\\\\\\\ S=\{-10;8\}$