78=14x+4x^2

Solution for 78=14x+4x^2 equation:

Simplifying
78 = 14x + 4x2

Solving
78 = 14x + 4x2

Solving for variable 'x'.

Reorder the terms:
78 + -14x + -4x2 = 14x + -14x + 4x2 + -4x2

Combine like terms: 14x + -14x = 0
78 + -14x + -4x2 = 0 + 4x2 + -4x2
78 + -14x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
78 + -14x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(39 + -7x + -2x2) = 0

Factor a trinomial.
2((3 + -1x)(13 + 2x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

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

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

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

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

Simplifying
x = 3
Subproblem 2
Set the factor '(13 + 2x)' equal to zero and attempt to solve:

Simplifying
13 + 2x = 0

Solving
13 + 2x = 0

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

Add '-13' to each side of the equation.
13 + -13 + 2x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 2x = 0 + -13
2x = 0 + -13

Combine like terms: 0 + -13 = -13
2x = -13

Divide each side by '2'.
x = -6.5

Simplifying
x = -6.5
Solution
x = {3, -6.5}