7x^2=8x-1

Solution for 7x^2=8x-1 equation:

Simplifying
7x2 = 8x + -1

Reorder the terms:
7x2 = -1 + 8x

Solving
7x2 = -1 + 8x

Solving for variable 'x'.

Reorder the terms:
1 + -8x + 7x2 = -1 + 8x + 1 + -8x

Reorder the terms:
1 + -8x + 7x2 = -1 + 1 + 8x + -8x

Combine like terms: -1 + 1 = 0
1 + -8x + 7x2 = 0 + 8x + -8x
1 + -8x + 7x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
1 + -8x + 7x2 = 0

Factor a trinomial.
(1 + -7x)(1 + -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 '(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 = {0.1428571429, 1}