3a^2-5a+7=5

Solution for 3a^2-5a+7=5 equation:

Simplifying
3a2 + -5a + 7 = 5

Reorder the terms:
7 + -5a + 3a2 = 5

Solving
7 + -5a + 3a2 = 5

Solving for variable 'a'.

Reorder the terms:
7 + -5 + -5a + 3a2 = 5 + -5

Combine like terms: 7 + -5 = 2
2 + -5a + 3a2 = 5 + -5

Combine like terms: 5 + -5 = 0
2 + -5a + 3a2 = 0

Factor a trinomial.
(2 + -3a)(1 + -1a) = 0

Subproblem 1
Set the factor '(2 + -3a)' equal to zero and attempt to solve:

Simplifying
2 + -3a = 0

Solving
2 + -3a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3a = 0 + -2
-3a = 0 + -2

Combine like terms: 0 + -2 = -2
-3a = -2

Divide each side by '-3'.
a = 0.6666666667

Simplifying
a = 0.6666666667
Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

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

Simplifying
a = 1
Solution
a = {0.6666666667, 1}