Answer
$ \left\{-\dfrac{7}{2},3\right\} $
Work Step by Step
Using $ax^2+bx+c=0,$ the given equation, $ 2x^2+x-21=0 $ has \begin{align*}a= 2 ,b= 1 ,\text{ and }c= -21 .\end{align*} Using $ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a} $ or the Quadratic Formula, then \begin{align*} \require{cancel}x&=\dfrac{-1\pm\sqrt{1^2-4(2)(-21)}}{2(2)} \\\\&= \dfrac{-1\pm\sqrt{1+168}}{4} \\\\&= \dfrac{-1\pm\sqrt{169}}{4} \\\\&= \dfrac{-1\pm\sqrt{13^2}}{4} \\\\&= \dfrac{-1\pm13}{4} \end{align*}\begin{array}{c|c} x=\dfrac{-1-13}{4} & x=\dfrac{-1+13}{4} \\\\ x=\dfrac{-14}{4} & x=\dfrac{12}{4} \\\\ x=\dfrac{\cancelto{-7}{-14}}{\cancelto24} & x=3. \\\\ x=-\dfrac{7}{2} \end{array} Hence, the solution set of $ 2x^2+x-21=0 $ is $ \left\{-\dfrac{7}{2},3\right\} $.
