EXPLANATION :
From the problem, we have the equation :
[tex]2v^2=-5v-2[/tex]Rewrite in the form av^2 + bv + c = 0
[tex]\begin{gathered} 2v^2=-5v-2 \\ 2v^2+5v+2=0 \end{gathered}[/tex]Using quadratic formula with a = 2, b = 5, and c = 2
[tex]\begin{gathered} v=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ v=\frac{-5\pm\sqrt{5^2-4(2)(2)}}{2(2)} \\ \\ v=\frac{-5\pm\sqrt{9}}{4} \\ \\ v=\frac{-5\pm3}{4} \\ \\ v=\frac{-5+3}{4}=-\frac{1}{2} \\ \\ v=\frac{-5-3}{4}=-2 \end{gathered}[/tex]ANSWER :
The solutions are v = -2 and -1/2
