using quadratic formula 3y2=6+7y

3 y^2 -7y - 6 = 0
When using the quadratic formaul to find y, a = 3, b = -7 and c = -6

y = [-b +/- sqrt (b^2 -4ac)]/2a
= {7 +/- sqrt (49 + 72)}/6
= {7 +/- 11)/6
= +3 or -2/3

To solve the equation 3y^2 = 6 + 7y using the quadratic formula, follow these steps:

1. Rewrite the equation in the form of ax^2 + bx + c = 0:
3y^2 - 7y - 6 = 0

2. Identify the values of a, b, and c:
a = 3
b = -7
c = -6

3. Plug these values into the quadratic formula:
y = [-b ± √(b^2 - 4ac)] / 2a

Substitute the values of a, b, and c:
y = [-(-7) ± √((-7)^2 - 4(3)(-6))] / (2 * 3)
y = [7 ± √(49 + 72)] / 6
y = [7 ± √121] / 6
y = [7 ± 11] / 6

4. Simplify the expression:
y = (7 + 11) / 6 or y = (7 - 11) / 6
y = 18 / 6 or y = -4 / 6
y = 3 or y = -2/3

Therefore, the equation 3y^2 = 6 + 7y has two solutions: y = 3 and y = -2/3.