5x^2-41x+78=0

Solution for 5x^2-41x+78=0 equation:

Simplifying
5x2 + -41x + 78 = 0

Reorder the terms:
78 + -41x + 5x2 = 0

Solving
78 + -41x + 5x2 = 0

Solving for variable 'x'.

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

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 '(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
Solution
x = {3, 5.2}