5y2-8y+2=-1

To solve the equation \( 5y^2 - 8y + 2 = -1 \), we first rearrange it to set it equal to zero:

\[ 5y^2 - 8y + 2 + 1 = 0 \] \[ 5y^2 - 8y + 3 = 0 \]

Next, we can use the quadratic formula to find the values of \( y \). The quadratic formula is given by:

\[ y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

In our case, \( a = 5 \), \( b = -8 \), and \( c = 3 \). We first calculate the discriminant \( b^2 - 4ac \):

\[ b^2 - 4ac = (-8)^2 - 4(5)(3) = 64 - 60 = 4 \]

Now we'll substitute these values into the quadratic formula:

\[ y = \frac{-(-8) \pm \sqrt{4}}{2 \cdot 5} \] \[ y = \frac{8 \pm 2}{10} \]

This gives us two possible solutions:

1. \( y = \frac{8 + 2}{10} = \frac{10}{10} = 1 \)
2. \( y = \frac{8 - 2}{10} = \frac{6}{10} = \frac{3}{5} \)

Thus, the solutions to the equation \( 5y^2 - 8y + 2 = -1 \) are:

\[ y = 1 \quad \text{and} \quad y = \frac{3}{5} \]