Question

qual o conjunto solução desta equação:
$\frac{x^{2} }{2} -1 = \frac{x}{3} +15$

Answer 1

$\frac{ x^{2} }{2} -1= \frac{x}{3} +15 \\ \\ mmc(2,3)=6 \\ \\ 3x^2-6=2x+90 \\ \\ 3x^2-2x-6-90=0 \\ \\ 3x^2-2x-96=0 \\ \\ a=3 \\ b=-2 \\ c=-96 \\ \\ \Delta=b^2-4ac \\ \Delta=(-2)^2-4(3)(-96) \\ \Delta=4+1152 \\ \Delta=1156 \\ \\ x= \frac{-b\pm \sqrt{\Delta} }{2a} \\ \\ x= \frac{-(-2)\pm \sqrt{1156} }{2.(3)} = \frac{2\pm34}{6} \\ \\ x'= \frac{2+34}{6} = \frac{36}{6} =6 \\ \\ x"= \frac{2-34}{6} =- \frac{32}{6} =- \frac{16}{3}$