84y^2+y-9=0

Solution for 84y^2+y-9=0 equation:

Simplifying
84y2 + y + -9 = 0

Reorder the terms:
-9 + y + 84y2 = 0

Solving
-9 + y + 84y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -3y)(9 + -28y) = 0

Subproblem 1
Set the factor '(-1 + -3y)' equal to zero and attempt to solve:

Simplifying
-1 + -3y = 0

Solving
-1 + -3y = 0

Move all terms containing y to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -3y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3y = 0 + 1
-3y = 0 + 1

Combine like terms: 0 + 1 = 1
-3y = 1

Divide each side by '-3'.
y = -0.3333333333

Simplifying
y = -0.3333333333
Subproblem 2
Set the factor '(9 + -28y)' equal to zero and attempt to solve:

Simplifying
9 + -28y = 0

Solving
9 + -28y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + -28y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -28y = 0 + -9
-28y = 0 + -9

Combine like terms: 0 + -9 = -9
-28y = -9

Divide each side by '-28'.
y = 0.3214285714

Simplifying
y = 0.3214285714
Solution
y = {-0.3333333333, 0.3214285714}