How many and what type of solutions does the equation have?

2c2=16c-32

two rational solutions

two irrational solutions

one rational solution

two nonreal solutions

To determine the type of solutions that a quadratic equation has we can solve this through the use of the discriminant. The discriminant is calculated through the equation,

D = b² - 4ac

where a, b, and c are the numerical coefficients of the terms of the quadratic expression.

D = (-16) ² - 4 (2) (-32) = 512

Since the discriminant is greater than zero, there are two rational roots.