Question

Resolução da equação: 12 - 4x (1-x) = x² - 2x - 7

Answer 1

$12-4x(1-x)=x^{2}-2x-7\\12-4x.1-4x.(-x)=x^{2}-2x-7\\12-4x+4x^{2}=x^{2}-2x-7\\4x^{2}-x^{2}-4x+2x+12+7=0\\3x^{2}-2x+19=0$

$\Delta=b^{2}-4ac\\\Delta=(-2)^{2}-4*3*19\\\Delta=4-228\\\Delta=-224\\\Delta=-1*16*14\\\sqrt{\Delta}=\sqrt{-1}*\sqrt{16}*\sqrt{14}\\\sqrt{\Delta}=i*4*\sqrt{14}\\\sqrt{\Delta}=4i\sqrt{14}$

$x=(-b\pm\sqrt{\Delta})/2a\\x=(-[-2]\pm4i\sqrt{14})/(2*3)\\x=(2\pm4i\sqrt{14})/(2*3)\\x=2*(1\pm2i\sqrt{14})/(2*3)\\x=(1\pm2i\sqrt{14})/3$

$x'=(1+2i\sqrt{14})/3\\x''=(1-2i\sqrt{14})/3$