#### Answer

The give equation has two complex number solutions.

#### Work Step by Step

Subtract $7$ to both sides to obtain:
$$-8x^2+10x-7=7-7
\\-8x^2+10x-7=0$$
This this equation has $a=-8$, $b=10$, and $c=-7$.
RECALL:
(1) The discriminant is equal to $b^2-4ac$.
(2) A quadratic equation has the following types of solutions based on the value of the discriminant:
(a) when $b^2-4ac\gt0$, the equation has two unequal rational solutions;
(b) when $b^2-4ac=0$, the equation has one, repeated rational solution; and
(c) when $b^2-4ac\lt0$, the equation has two complex number solutions;
The discriminant of the equation above is:
$$b^2-4ac = 10^2 - 4(-8)(-7) = 100-224=-124$$
The discriminant is negative.
Thus, the give equation has two complex number solutions.