0=140-51a+4a^2

Solution for 0=140-51a+4a^2 equation:

Simplifying
0 = 140 + -51a + 4a2

Solving
0 = 140 + -51a + 4a2

Solving for variable 'a'.

Combine like terms: 0 + -140 = -140
-140 + 51a + -4a2 = 140 + -51a + 4a2 + -140 + 51a + -4a2

Reorder the terms:
-140 + 51a + -4a2 = 140 + -140 + -51a + 51a + 4a2 + -4a2

Combine like terms: 140 + -140 = 0
-140 + 51a + -4a2 = 0 + -51a + 51a + 4a2 + -4a2
-140 + 51a + -4a2 = -51a + 51a + 4a2 + -4a2

Combine like terms: -51a + 51a = 0
-140 + 51a + -4a2 = 0 + 4a2 + -4a2
-140 + 51a + -4a2 = 4a2 + -4a2

Combine like terms: 4a2 + -4a2 = 0
-140 + 51a + -4a2 = 0

Factor a trinomial.
(-35 + 4a)(4 + -1a) = 0

Subproblem 1
Set the factor '(-35 + 4a)' equal to zero and attempt to solve:

Simplifying
-35 + 4a = 0

Solving
-35 + 4a = 0

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

Add '35' to each side of the equation.
-35 + 35 + 4a = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 4a = 0 + 35
4a = 0 + 35

Combine like terms: 0 + 35 = 35
4a = 35

Divide each side by '4'.
a = 8.75

Simplifying
a = 8.75
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 = {8.75, 4}