2u^2=7u+4

Solution for 2u^2=7u+4 equation:

Simplifying
2u2 = 7u + 4

Reorder the terms:
2u2 = 4 + 7u

Solving
2u2 = 4 + 7u

Solving for variable 'u'.

Reorder the terms:
-4 + -7u + 2u2 = 4 + 7u + -4 + -7u

Reorder the terms:
-4 + -7u + 2u2 = 4 + -4 + 7u + -7u

Combine like terms: 4 + -4 = 0
-4 + -7u + 2u2 = 0 + 7u + -7u
-4 + -7u + 2u2 = 7u + -7u

Combine like terms: 7u + -7u = 0
-4 + -7u + 2u2 = 0

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

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

Simplifying
-1 + -2u = 0

Solving
-1 + -2u = 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 + -2u = 0 + 1

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

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

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

Simplifying
u = -0.5
Subproblem 2
Set the factor '(4 + -1u)' equal to zero and attempt to solve:

Simplifying
4 + -1u = 0

Solving
4 + -1u = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1u = 0 + -4
-1u = 0 + -4

Combine like terms: 0 + -4 = -4
-1u = -4

Divide each side by '-1'.
u = 4

Simplifying
u = 4
Solution
u = {-0.5, 4}