5x^2+11x-78=0

Solution for 5x^2+11x-78=0 equation:

Simplifying
5x2 + 11x + -78 = 0

Reorder the terms:
-78 + 11x + 5x2 = 0

Solving
-78 + 11x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-26 + -5x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-26 + -5x)' equal to zero and attempt to solve:

Simplifying
-26 + -5x = 0

Solving
-26 + -5x = 0

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

Add '26' to each side of the equation.
-26 + 26 + -5x = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -5x = 0 + 26
-5x = 0 + 26

Combine like terms: 0 + 26 = 26
-5x = 26

Divide each side by '-5'.
x = -5.2

Simplifying
x = -5.2
Subproblem 2
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
Solution
x = {-5.2, 3}