Question 19277
Hello There:

The quadratic formula solves equations in the form of:

a*x^2 + b*x + c = 0  when you're given the values of a, b, and c.

In your equation we have a = 3, b = -4, and c = -5.

The quadratic formula is:

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

Substitute the given values for a, b, and c.

x = [-(-4) +/- sqrt(4^2 - 4*3*[-5])]/[2*3]

x = [4 +/- sqrt(16 + 60)]/6

x = [4 +/- sqrt(76)]/6

Since 76 = 2*2*19, the square root of 76 simplifies to 2*sqrt(19)

x = [4 +/- 2*sqrt(19)]/6

There are two solutions.

x = 4/6 + 2*sqrt(19)/6 and x = 4/6 - 2*sqrt(19)/6

x = 2/3 + sqrt(19)/3

x = 2/3 - sqrt(19)/3

~ Mark