8f^2+100f-52=0

Solution for 8f^2+100f-52=0 equation:

Simplifying
8f2 + 100f + -52 = 0

Reorder the terms:
-52 + 100f + 8f2 = 0

Solving
-52 + 100f + 8f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-13 + 25f + 2f2) = 0

Factor a trinomial.
4((-13 + -1f)(1 + -2f)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-13 + -1f)' equal to zero and attempt to solve:

Simplifying
-13 + -1f = 0

Solving
-13 + -1f = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1f = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1f = 0 + 13
-1f = 0 + 13

Combine like terms: 0 + 13 = 13
-1f = 13

Divide each side by '-1'.
f = -13

Simplifying
f = -13
Subproblem 2
Set the factor '(1 + -2f)' equal to zero and attempt to solve:

Simplifying
1 + -2f = 0

Solving
1 + -2f = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2f = 0 + -1

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

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

Divide each side by '-2'.
f = 0.5

Simplifying
f = 0.5
Solution
f = {-13, 0.5}