5x^2=7x-2

Solution for 5x^2=7x-2 equation:

Simplifying
5x2 = 7x + -2

Reorder the terms:
5x2 = -2 + 7x

Solving
5x2 = -2 + 7x

Solving for variable 'x'.

Reorder the terms:
2 + -7x + 5x2 = -2 + 7x + 2 + -7x

Reorder the terms:
2 + -7x + 5x2 = -2 + 2 + 7x + -7x

Combine like terms: -2 + 2 = 0
2 + -7x + 5x2 = 0 + 7x + -7x
2 + -7x + 5x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
2 + -7x + 5x2 = 0

Factor a trinomial.
(2 + -5x)(1 + -1x) = 0

Subproblem 1
Set the factor '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 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 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
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 = {0.4, 1}