Question

o dobro do quadrado de um número mais o dobro desse número menos 24 e igual a

Answer 1

$2x^2+2x-24=0\\\\ 2\cdot (x^2+x-12)=0\\\\ x^2+x-12=0~~~\Rightarrow~~\left\{\!\begin{array}{l} a=1\\b=1\\c=-12 \end{array}\right.\\\\\\\\ \Delta=b^2-4ac\\\\ \Delta=1^2-4\cdot 1\cdot (-12)\\\\ \Delta=1+48\\\\ \Delta=49=7^2$


$x=\dfrac{-b\pm \sqrt{\Delta}}{2a}\\\\\\ x=\dfrac{-1\pm \sqrt{7^2}}{2\cdot 1}\\\\\\ x=\dfrac{-1\pm 7}{2}\\\\\\ \begin{array}{rcl} x=\dfrac{-1-7}{2}&~\text{ ou }~&x=\dfrac{-1+7}{2}\\\\\\ x=\dfrac{-8}{2}&~\text{ ou }~&x=\dfrac{6}{2} \end{array}\\\\\\ ~~~~~\boxed{\begin{array}{c}\begin{array}{rcl} x=-4&~\text{ ou }~&x=3 \end{array} \end{array}}$


Bons estudos! :-)