5u^2=14u+3

Solution for 5u^2=14u+3 equation:

Simplifying
5u2 = 14u + 3

Reorder the terms:
5u2 = 3 + 14u

Solving
5u2 = 3 + 14u

Solving for variable 'u'.

Reorder the terms:
-3 + -14u + 5u2 = 3 + 14u + -3 + -14u

Reorder the terms:
-3 + -14u + 5u2 = 3 + -3 + 14u + -14u

Combine like terms: 3 + -3 = 0
-3 + -14u + 5u2 = 0 + 14u + -14u
-3 + -14u + 5u2 = 14u + -14u

Combine like terms: 14u + -14u = 0
-3 + -14u + 5u2 = 0

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

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

Simplifying
-1 + -5u = 0

Solving
-1 + -5u = 0

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

Add '1' to each side of the equation.
-1 + 1 + -5u = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5u = 0 + 1
-5u = 0 + 1

Combine like terms: 0 + 1 = 1
-5u = 1

Divide each side by '-5'.
u = -0.2

Simplifying
u = -0.2
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 = {-0.2, 3}