13x^2+7x=20

Solution for 13x^2+7x=20 equation:

Simplifying
13x2 + 7x = 20

Reorder the terms:
7x + 13x2 = 20

Solving
7x + 13x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + 7x + 13x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 7x + 13x2 = 0

Factor a trinomial.
(-20 + -13x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-20 + -13x)' equal to zero and attempt to solve:

Simplifying
-20 + -13x = 0

Solving
-20 + -13x = 0

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

Add '20' to each side of the equation.
-20 + 20 + -13x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -13x = 0 + 20
-13x = 0 + 20

Combine like terms: 0 + 20 = 20
-13x = 20

Divide each side by '-13'.
x = -1.538461538

Simplifying
x = -1.538461538
Subproblem 2
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
Solution
x = {-1.538461538, 1}