3u^2=4u+15

Solution for 3u^2=4u+15 equation:

Simplifying
3u2 = 4u + 15

Reorder the terms:
3u2 = 15 + 4u

Solving
3u2 = 15 + 4u

Solving for variable 'u'.

Reorder the terms:
-15 + -4u + 3u2 = 15 + 4u + -15 + -4u

Reorder the terms:
-15 + -4u + 3u2 = 15 + -15 + 4u + -4u

Combine like terms: 15 + -15 = 0
-15 + -4u + 3u2 = 0 + 4u + -4u
-15 + -4u + 3u2 = 4u + -4u

Combine like terms: 4u + -4u = 0
-15 + -4u + 3u2 = 0

Factor a trinomial.
(-5 + -3u)(3 + -1u) = 0

Subproblem 1
Set the factor '(-5 + -3u)' equal to zero and attempt to solve:

Simplifying
-5 + -3u = 0

Solving
-5 + -3u = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3u = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3u = 0 + 5
-3u = 0 + 5

Combine like terms: 0 + 5 = 5
-3u = 5

Divide each side by '-3'.
u = -1.666666667

Simplifying
u = -1.666666667
Subproblem 2
Set the factor '(3 + -1u)' equal to zero and attempt to solve:

Simplifying
3 + -1u = 0

Solving
3 + -1u = 0

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

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

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

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

Divide each side by '-1'.
u = 3

Simplifying
u = 3
Solution
u = {-1.666666667, 3}