which expression gives the solutions of -5+2x^2=-6x?

Taking 2x² + 6x - 5  =  0 and using the on-site calculator, we have....

$${\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{5}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{19}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}\right)}{{\mathtt{2}}}}\\
{\mathtt{x}} = {\frac{\left({\sqrt{{\mathtt{19}}}}{\mathtt{\,-\,}}{\mathtt{3}}\right)}{{\mathtt{2}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{3.679\: \!449\: \!471\: \!770\: \!336\: \!8}}\\
{\mathtt{x}} = {\mathtt{0.679\: \!449\: \!471\: \!770\: \!336\: \!8}}\\
\end{array} \right\}$$

Rearrange the terms on the left side:

2x² - 5  =  -6x

Add 6x to both sides:

2x² + 6x - 5  =  0

This is not easily factored; so I would suggest that you use the quadratic formula:

  x  =  [ -b ± √( b² - 4ac ) ] / ( 2a )

where, for this problem,  a = 2,  b = 6,  and  c = -5.