Solve the equation 8y2+54y+81=0.

Sure, let's solve the quadratic equation step by step.

The given equation is 8y^2 + 54y + 81 = 0.

Step 1: Identify the coefficients a, b, and c in the equation, which are 8, 54, and 81 respectively.

Step 2: Calculate the discriminant using the formula D = b^2 - 4ac.

Substituting the values, we get D = (54)^2 - 4881 = 2916 - 2592 = 324.

Step 3: Find the square root of the discriminant √D. The square root of 324 is 18.

Step 4: Use the quadratic formula to find the roots of the equation. The quadratic formula is y = [-b ± √D] / 2a.

Substituting the values, we get y = [-54 ± 18] / (2*8).

So, the roots of the equation are y1 = (-54 + 18) / 16 = -2.25 and y2 = (-54 - 18) / 16 = -4.5.

Therefore, the solutions to the equation 8y^2 + 54y + 81 = 0 are y = -2.25 and y = -4.5.