3a^2=7a+20

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

Simplifying
3a2 = 7a + 20

Reorder the terms:
3a2 = 20 + 7a

Solving
3a2 = 20 + 7a

Solving for variable 'a'.

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

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

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

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

Factor a trinomial.
(-5 + -3a)(4 + -1a) = 0

Subproblem 1
Set the factor '(-5 + -3a)' equal to zero and attempt to solve:

Simplifying
-5 + -3a = 0

Solving
-5 + -3a = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3a = 0 + 5

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

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

Divide each side by '-3'.
a = -1.666666667

Simplifying
a = -1.666666667
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 = {-1.666666667, 4}