7a^2=20a+3

Solution for 7a^2=20a+3 equation:

Simplifying
7a2 = 20a + 3

Reorder the terms:
7a2 = 3 + 20a

Solving
7a2 = 3 + 20a

Solving for variable 'a'.

Reorder the terms:
-3 + -20a + 7a2 = 3 + 20a + -3 + -20a

Reorder the terms:
-3 + -20a + 7a2 = 3 + -3 + 20a + -20a

Combine like terms: 3 + -3 = 0
-3 + -20a + 7a2 = 0 + 20a + -20a
-3 + -20a + 7a2 = 20a + -20a

Combine like terms: 20a + -20a = 0
-3 + -20a + 7a2 = 0

Factor a trinomial.
(-1 + -7a)(3 + -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 '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-0.1428571429, 3}