Answer
The solutions are $x=\frac{3-\sqrt{65}}{4}$ and $x=\frac{3+\sqrt{65}}{4}$.
Work Step by Step
The given equation is
$\Rightarrow -2x^2+3x+7=0$
The equation is no factorable. So, solve by quadratic formula.
Quadratic formula is
$\Rightarrow x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute $-2$ for $a,3$ for $b$ and $7$ for $c$.
$\Rightarrow x=\frac{-3\pm\sqrt{3^2-4(-2)(7)}}{2(-2)}$
Clear the parentheses.
$\Rightarrow x=\frac{-3\pm\sqrt{9+56}}{-4}$
Simplify.
$\Rightarrow x=\frac{-3\pm\sqrt{65}}{-4}$
Hence, the solutions are $x=\frac{-3+\sqrt{65}}{-4}=\frac{3-\sqrt{65}}{4}$ and $x=\frac{-3-\sqrt{65}}{-4}=\frac{3+\sqrt{65}}{4}$.
