Answer
$x=-\dfrac{7}{2}\pm\dfrac{\sqrt{51}}{2}$
Work Step by Step
Using the completing the square method, then,
\begin{array}{l}
2x^2+14x-1=0\\
x^2+7x-\dfrac{1}{2}=0\\
x^2+7x=\dfrac{1}{2}\\
x^2+7x+\left( \dfrac{7}{2} \right)^2=\dfrac{1}{2}+\left( \dfrac{7}{2}\right)^2\\
x^2+7x+\dfrac{49}{4}=\dfrac{1}{2}+\dfrac{49}{4}\\
\left( x+\dfrac{7}{2} \right)^2=\dfrac{51}{4}\\
x+\dfrac{7}{2}=\pm\sqrt{\dfrac{51}{4}}\\
x=-\dfrac{7}{2}\pm\dfrac{\sqrt{51}}{2}
.\end{array}
