Solve the following equation. (Examples 1-6)

15x2 = -17x + 4
x = 1 (smaller value)
x = 2 (larger value)

To solve the equation 15x^2 = -17x + 4, we will use the quadratic formula.

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / 2a

In our equation, we have:

a = 15
b = -17
c = 4

Substituting the values into the quadratic formula, we get:

x = (-(-17) ± √((-17)^2 - 4(15)(4))) / (2(15))

Simplifying further:

x = (17 ± √(289 - 240)) / 30

x = (17 ± √49) / 30

Taking the square root of 49:

x = (17 ± 7) / 30

Now, we have two solutions:
1. For x = (17 + 7) / 30 = 24 / 30 = 4 / 5 = 0.8
2. For x = (17 - 7) / 30 = 10 / 30 = 1 / 3 ≈ 0.333

So, the solutions to the equation are:
1. x = 0.8
2. x ≈ 0.333

The smaller value of x is 0.333 (rounded to three decimal places), and the larger value is 0.8.