Question

Encontre as raízes reais da equação
2m² - m - 6 = 0

Answer 1

m²-m-12=0
(m+3/2)(m-4/2)
m=-3/2 ou m=2

Answer 2

$2m^2-m-6=0\\\\ a=2;\ b=-1;\ c=-6\\\\\\ \Delta=b^2-4ac\to \Delta=(-1)^2-4.2.(-6)\to \Delta=1+48\to \boxed{\Delta=49}\\\\ x' \neq x''\\\\\\\ x= \frac{-b\pm \sqrt{ \Delta} }{2a} \to x= \frac{-(-1)\pm \sqrt{ 49} }{2.2} \to x= \frac{1\pm7 }{4} \to \\\\\\ x'= \frac{1+7 }{4} \to x'= \frac{8 }{4} \to \boxed{x'= 2} \\\\\\ x''= \dfrac{1-7 }{4} \to x''= \dfrac{-6}{4} \to \boxed{x''=- \frac{3}{2} }\\\\\\\\ \boxed{\boxed{S=\{-\frac{3}{2};2 \}}}$