How many real number solutions does the equation have? y=-5x^2+8x-7

The nature of the solutions/roots of a quadratic function can be determined from its discriminant. 

The discriminant of a quadratic function can be calculated as:

Discriminant = b² - 4ac

Here,
a = coefficient of squared term = -5
b = coefficient of x term = 8
c = constant = - 7

So, the discriminant will be:

Discriminant = 64 - 4(-5)(-7) = - 76

The value of the discriminant is negative. This shows that the given quadratic function has no real solution.