A small company borrows money and remains in debt to its lenders for a period of time. The function f (x) = - 6x2+8x+50 represents the amount of debt the company has, in thousands of dollars, x years after opening its business. Approximately how many years after opening its business will the company be out of debt?

A. 2.9

B. 3.2

C. 3.6

D. 4.2

Given that the debt has been represented by the function:

f (x) = - 6x^2+8x+50

To get the number of years, x that it would take for the company to be debt free we proceed as follows:

we solve the equation for f (x) = 0

hence:

0=-6x^2+8x+50

solving for x using the quadratic formula we get:

x=[-b+/-sqrt (b^2-4ac) ]/2a

x=[-8+/-sqrt (8^2-4 * (-6) * 50) ] / (-6*2)

x=[-8+/-√1264] / (-12)

x=27.552

x~28