7a^2=29a-4

Solution for 7a^2=29a-4 equation:

Simplifying
7a2 = 29a + -4

Reorder the terms:
7a2 = -4 + 29a

Solving
7a2 = -4 + 29a

Solving for variable 'a'.

Reorder the terms:
4 + -29a + 7a2 = -4 + 29a + 4 + -29a

Reorder the terms:
4 + -29a + 7a2 = -4 + 4 + 29a + -29a

Combine like terms: -4 + 4 = 0
4 + -29a + 7a2 = 0 + 29a + -29a
4 + -29a + 7a2 = 29a + -29a

Combine like terms: 29a + -29a = 0
4 + -29a + 7a2 = 0

Factor a trinomial.
(1 + -7a)(4 + -1a) = 0

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

Simplifying
1 + -7a = 0

Solving
1 + -7a = 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 + -7a = 0 + -1

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

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

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

Simplifying
a = 0.1428571429
Subproblem 2
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {0.1428571429, 4}