3946=0.5*10*v^2+10*9.82*8

Solution for 3946=0.5*10*v^2+10*9.82*8 equation:

Simplifying
3946 = 0.5 * 10v2 + 10 * 9.82 * 8

Multiply 0.5 * 10
3946 = 5v2 + 10 * 9.82 * 8

Multiply 10 * 9.82
3946 = 5v2 + 98.2 * 8

Multiply 98.2 * 8
3946 = 5v2 + 785.6

Reorder the terms:
3946 = 785.6 + 5v2

Solving
3946 = 785.6 + 5v2

Solving for variable 'v'.

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

Add '-5v2' to each side of the equation.
3946 + -5v2 = 785.6 + 5v2 + -5v2

Combine like terms: 5v2 + -5v2 = 0
3946 + -5v2 = 785.6 + 0
3946 + -5v2 = 785.6

Add '-3946' to each side of the equation.
3946 + -3946 + -5v2 = 785.6 + -3946

Combine like terms: 3946 + -3946 = 0
0 + -5v2 = 785.6 + -3946
-5v2 = 785.6 + -3946

Combine like terms: 785.6 + -3946 = -3160.4
-5v2 = -3160.4

Divide each side by '-5'.
v2 = 632.08

Simplifying
v2 = 632.08

Take the square root of each side:
v = {-25.141201244, 25.141201244}