0=4x^2-45x+116

Solution for 0=4x^2-45x+116 equation:

Simplifying
0 = 4x2 + -45x + 116

Reorder the terms:
0 = 116 + -45x + 4x2

Solving
0 = 116 + -45x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + -116 = -116
-116 + 45x + -4x2 = 116 + -45x + 4x2 + -116 + 45x + -4x2

Reorder the terms:
-116 + 45x + -4x2 = 116 + -116 + -45x + 45x + 4x2 + -4x2

Combine like terms: 116 + -116 = 0
-116 + 45x + -4x2 = 0 + -45x + 45x + 4x2 + -4x2
-116 + 45x + -4x2 = -45x + 45x + 4x2 + -4x2

Combine like terms: -45x + 45x = 0
-116 + 45x + -4x2 = 0 + 4x2 + -4x2
-116 + 45x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-116 + 45x + -4x2 = 0

Factor a trinomial.
(-29 + 4x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-29 + 4x)' equal to zero and attempt to solve:

Simplifying
-29 + 4x = 0

Solving
-29 + 4x = 0

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

Add '29' to each side of the equation.
-29 + 29 + 4x = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 4x = 0 + 29
4x = 0 + 29

Combine like terms: 0 + 29 = 29
4x = 29

Divide each side by '4'.
x = 7.25

Simplifying
x = 7.25
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

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

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

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

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

Simplifying
x = 4
Solution
x = {7.25, 4}