7x^2=13x+2

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

Simplifying
7x2 = 13x + 2

Reorder the terms:
7x2 = 2 + 13x

Solving
7x2 = 2 + 13x

Solving for variable 'x'.

Reorder the terms:
-2 + -13x + 7x2 = 2 + 13x + -2 + -13x

Reorder the terms:
-2 + -13x + 7x2 = 2 + -2 + 13x + -13x

Combine like terms: 2 + -2 = 0
-2 + -13x + 7x2 = 0 + 13x + -13x
-2 + -13x + 7x2 = 13x + -13x

Combine like terms: 13x + -13x = 0
-2 + -13x + 7x2 = 0

Factor a trinomial.
(-1 + -7x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-1 + -7x)' equal to zero and attempt to solve:

Simplifying
-1 + -7x = 0

Solving
-1 + -7x = 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 + -7x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7x = 0 + 1
-7x = 0 + 1

Combine like terms: 0 + 1 = 1
-7x = 1

Divide each side by '-7'.
x = -0.1428571429

Simplifying
x = -0.1428571429
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 = {-0.1428571429, 2}