5a^2+7a=34

Solution for 5a^2+7a=34 equation:

Simplifying
5a2 + 7a = 34

Reorder the terms:
7a + 5a2 = 34

Solving
7a + 5a2 = 34

Solving for variable 'a'.

Reorder the terms:
-34 + 7a + 5a2 = 34 + -34

Combine like terms: 34 + -34 = 0
-34 + 7a + 5a2 = 0

Factor a trinomial.
(-17 + -5a)(2 + -1a) = 0

Subproblem 1
Set the factor '(-17 + -5a)' equal to zero and attempt to solve:

Simplifying
-17 + -5a = 0

Solving
-17 + -5a = 0

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

Add '17' to each side of the equation.
-17 + 17 + -5a = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -5a = 0 + 17
-5a = 0 + 17

Combine like terms: 0 + 17 = 17
-5a = 17

Divide each side by '-5'.
a = -3.4

Simplifying
a = -3.4
Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 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 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-3.4, 2}