Final answer:
The quadratic equation -5x^2+3x-10=0 has no real solutions because the discriminant, calculated as b^2 - 4ac, is negative.
Step-by-step explanation:
To determine how many real solutions the quadratic equation -5x2+3x-10=0 has, we can apply the discriminant method using the quadratic formula, ax2+bx+c=0. The discriminant (D) is part of the quadratic formula and is found by the expression D = b2 - 4ac. In this equation, a=-5, b=3, and c=-10. Thus, the discriminant is D = (3)2 - 4(-5)(-10) = 9 - 200 = -191. Since the discriminant is negative (D < 0), there are no real solutions to this quadratic equation.