Question

resolva a equação do segundo grau:
 
a)  -3 =   x   (1- x )
             6   (    3 )

Answer 1

$-3= \frac{x}{6}( \frac{1-x}{3})\\\\ -3= \frac{x(1-x)}{6*3}\\\\ -3= \frac{ -x^{2}+x }{18}\\\\ (-3).18=- x^{2} +x\\ - x^{2} +x=-54\\ x^{2} -x-54=0$

Vamos aplicar Báskara:

$\Delta=b ^{2}-4ac\\ \Delta=(-1) ^{2}-4*1*(-54)\\ \Delta=1+216\\ \Delta=217$

$\boxed{x= \frac{-b\pm \sqrt{\Delta} }{2a}}$

$x= \frac{-1\pm \sqrt{217} }{2*1}~\to~x= \frac{-1\pm \sqrt{217} }{2}\\\\ \boxed{S=\{ \frac{-1+ \sqrt{217} }{ 2 },~ \frac{-1- \sqrt{217} }{2}\}}$


Espero ter ajudado e tenha ótimos estudos =)