solve each equation

1/5y2-2=-3y

To solve the equation 1/5y^2 - 2 = -3y, we can follow these steps:

Step 1: Move all terms to one side of the equation to set it equal to zero.
Rearrange the equation: 1/5y^2 - 3y - 2 = 0

Step 2: Multiply every term by 5 to eliminate the fraction. This will help us work with whole numbers.
5 * (1/5y^2 - 3y - 2) = 5 * 0
y^2 - 15y - 10 = 0

Step 3: Solve the quadratic equation.
There are different methods to solve a quadratic equation. Let's use the quadratic formula:
y = (-b ± √(b^2 - 4ac)) / (2a)

In our equation, we have a = 1, b = -15, and c = -10. Plugging in these values:
y = (-(-15) ± √((-15)^2 - 4(1)(-10))) / (2(1))
y = (15 ± √(225 + 40)) / 2
y = (15 ± √(265)) / 2

So the two possible solutions for y are:
y = (15 + √(265)) / 2
y = (15 - √(265)) / 2