13x^2+4x-9=0

Solution for 13x^2+4x-9=0 equation:

Simplifying
13x2 + 4x + -9 = 0

Reorder the terms:
-9 + 4x + 13x2 = 0

Solving
-9 + 4x + 13x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -1x)(9 + -13x) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(9 + -13x)' equal to zero and attempt to solve:

Simplifying
9 + -13x = 0

Solving
9 + -13x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -13x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -13x = 0 + -9
-13x = 0 + -9

Combine like terms: 0 + -9 = -9
-13x = -9

Divide each side by '-13'.
x = 0.6923076923

Simplifying
x = 0.6923076923
Solution
x = {-1, 0.6923076923}