9.81*0.5*(7.9-x)*(7.9-x)=340*x

Solution for 9.81*0.5*(7.9-x)*(7.9-x)=340*x equation:

Simplifying
9.81 * 0.5(7.9 + -1x)(7.9 + -1x) = 340x

Multiply 9.81 * 0.5
4.905(7.9 + -1x)(7.9 + -1x) = 340x

Multiply (7.9 + -1x) * (7.9 + -1x)
4.905(7.9(7.9 + -1x) + -1x * (7.9 + -1x)) = 340x
4.905((7.9 * 7.9 + -1x * 7.9) + -1x * (7.9 + -1x)) = 340x
4.905((62.41 + -7.9x) + -1x * (7.9 + -1x)) = 340x
4.905(62.41 + -7.9x + (7.9 * -1x + -1x * -1x)) = 340x
4.905(62.41 + -7.9x + (-7.9x + 1x2)) = 340x

Combine like terms: -7.9x + -7.9x = -15.8x
4.905(62.41 + -15.8x + 1x2) = 340x
(62.41 * 4.905 + -15.8x * 4.905 + 1x2 * 4.905) = 340x
(306.12105 + -77.499x + 4.905x2) = 340x

Solving
306.12105 + -77.499x + 4.905x2 = 340x

Solving for variable 'x'.

Reorder the terms:
306.12105 + -77.499x + -340x + 4.905x2 = 340x + -340x

Combine like terms: -77.499x + -340x = -417.499x
306.12105 + -417.499x + 4.905x2 = 340x + -340x

Combine like terms: 340x + -340x = 0
306.12105 + -417.499x + 4.905x2 = 0

Begin completing the square.  Divide all terms by
4.905 the coefficient of the squared term: 

Divide each side by '4.905'.
62.41 + -85.11702345x + x2 = 0

Move the constant term to the right:

Add '-62.41' to each side of the equation.
62.41 + -85.11702345x + -62.41 + x2 = 0 + -62.41

Reorder the terms:
62.41 + -62.41 + -85.11702345x + x2 = 0 + -62.41

Combine like terms: 62.41 + -62.41 = 0.00
0.00 + -85.11702345x + x2 = 0 + -62.41
-85.11702345x + x2 = 0 + -62.41

Combine like terms: 0 + -62.41 = -62.41
-85.11702345x + x2 = -62.41

The x term is -85.11702345x.  Take half its coefficient (-42.55851173).
Square it (1811.226921) and add it to both sides.

Add '1811.226921' to each side of the equation.
-85.11702345x + 1811.226921 + x2 = -62.41 + 1811.226921

Reorder the terms:
1811.226921 + -85.11702345x + x2 = -62.41 + 1811.226921

Combine like terms: -62.41 + 1811.226921 = 1748.816921
1811.226921 + -85.11702345x + x2 = 1748.816921

Factor a perfect square on the left side:
(x + -42.55851173)(x + -42.55851173) = 1748.816921

Calculate the square root of the right side: 41.818858437

Break this problem into two subproblems by setting 
(x + -42.55851173) equal to 41.818858437 and -41.818858437.

Subproblem 1
x + -42.55851173 = 41.818858437

Simplifying
x + -42.55851173 = 41.818858437

Reorder the terms:
-42.55851173 + x = 41.818858437

Solving
-42.55851173 + x = 41.818858437

Solving for variable 'x'.

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

Add '42.55851173' to each side of the equation.
-42.55851173 + 42.55851173 + x = 41.818858437 + 42.55851173

Combine like terms: -42.55851173 + 42.55851173 = 0.00000000
0.00000000 + x = 41.818858437 + 42.55851173
x = 41.818858437 + 42.55851173

Combine like terms: 41.818858437 + 42.55851173 = 84.377370167
x = 84.377370167

Simplifying
x = 84.377370167

Subproblem 2
x + -42.55851173 = -41.818858437

Simplifying
x + -42.55851173 = -41.818858437

Reorder the terms:
-42.55851173 + x = -41.818858437

Solving
-42.55851173 + x = -41.818858437

Solving for variable 'x'.

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

Add '42.55851173' to each side of the equation.
-42.55851173 + 42.55851173 + x = -41.818858437 + 42.55851173

Combine like terms: -42.55851173 + 42.55851173 = 0.00000000
0.00000000 + x = -41.818858437 + 42.55851173
x = -41.818858437 + 42.55851173

Combine like terms: -41.818858437 + 42.55851173 = 0.739653293
x = 0.739653293

Simplifying
x = 0.739653293

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {84.377370167, 0.739653293}