10y^2=3y+4

Solution for 10y^2=3y+4 equation:

Simplifying
10y2 = 3y + 4

Reorder the terms:
10y2 = 4 + 3y

Solving
10y2 = 4 + 3y

Solving for variable 'y'.

Reorder the terms:
-4 + -3y + 10y2 = 4 + 3y + -4 + -3y

Reorder the terms:
-4 + -3y + 10y2 = 4 + -4 + 3y + -3y

Combine like terms: 4 + -4 = 0
-4 + -3y + 10y2 = 0 + 3y + -3y
-4 + -3y + 10y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
-4 + -3y + 10y2 = 0

Factor a trinomial.
(-1 + -2y)(4 + -5y) = 0

Subproblem 1
Set the factor '(-1 + -2y)' equal to zero and attempt to solve:

Simplifying
-1 + -2y = 0

Solving
-1 + -2y = 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 + -2y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2y = 0 + 1
-2y = 0 + 1

Combine like terms: 0 + 1 = 1
-2y = 1

Divide each side by '-2'.
y = -0.5

Simplifying
y = -0.5
Subproblem 2
Set the factor '(4 + -5y)' equal to zero and attempt to solve:

Simplifying
4 + -5y = 0

Solving
4 + -5y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5y = 0 + -4
-5y = 0 + -4

Combine like terms: 0 + -4 = -4
-5y = -4

Divide each side by '-5'.
y = 0.8

Simplifying
y = 0.8
Solution
y = {-0.5, 0.8}