4x^2+54x-124=0

Solution for 4x^2+54x-124=0 equation:

Simplifying
4x2 + 54x + -124 = 0

Reorder the terms:
-124 + 54x + 4x2 = 0

Solving
-124 + 54x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-62 + 27x + 2x2) = 0

Factor a trinomial.
2((-31 + -2x)(2 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-31 + -2x)' equal to zero and attempt to solve:

Simplifying
-31 + -2x = 0

Solving
-31 + -2x = 0

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

Add '31' to each side of the equation.
-31 + 31 + -2x = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -2x = 0 + 31
-2x = 0 + 31

Combine like terms: 0 + 31 = 31
-2x = 31

Divide each side by '-2'.
x = -15.5

Simplifying
x = -15.5
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-15.5, 2}