11y 2 −12y+4=6y 2

Sure, let's solve the equation step by step:

Given equation is: 11y^2 - 12y + 4 = 6y^2

Step 1: Subtract 6y^2 from both sides to bring all the y terms on one side. This gives us:

11y^2 - 6y^2 - 12y + 4 = 0

Step 2: Simplify the equation:

5y^2 - 12y + 4 = 0

This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 5, b = -12, and c = 4.

Step 3: Solve for y using the quadratic formula y = [-b ± sqrt(b^2 - 4ac)] / (2a):

y = [12 ± sqrt((-12)^2 - 454)] / (2*5)

Step 4: Simplify under the square root:

y = [12 ± sqrt(144 - 80)] / 10

Step 5: Simplify further:

y = [12 ± sqrt(64)] / 10

Step 6: Take the square root of 64:

y = [12 ± 8] / 10

Step 7: Solve for y:

y = 20/10 or y = 4/10

So, the solutions for y are y = 2 and y = 0.4.