f(x)= -6x^2 + 9x + 5

Question

I am having a hard time finding the two soltuions to this problem after setting it to 0

Answer 1

Whenever you have a quadratic problem you can't factor easily, I recommend using the quadratic formula. This will allow you to solve any equation of the form ax^2 + bx + c = 0.

 

In your case, a = -6, b = 9, and c = 5.

 

The quadratic formula is as follows:

 

x = (-b ± √(b^2 - 4ac))/(2a)

 

If you plug in your values for a, b, and c, it should spit out two x values that will give you zero. These are the solutions to your problem.

 

Best of luck!

Answer 2

For this one you'll have to use the quadratic formula, which is x = -b +/- )sqroot (b² - 4ac)) / 2a. 

 

The standard form which this equation is in, Ax² + Bx + C = 0, gives us the values for a, b, and c. So in this case, A = -6, B = 9, and C = 5. 

 

Plug those numbers into the quadratic formula

x = -9 +/- (squareroot ( (9² - 4(-6)(5))) / 2(-6)     =  -9 +/- (sqrt (81 - (-120)) / -12  

= -9 +/- (sqrt ( 81 + 120)) / -12

 

= -9 +/- sqrt (201) / -12 

 

Your two answers are the answer above, one with the plus sign, and one with the negative sign.