3x(x-70)=5

Solution for 3x(x-70)=5 equation:

Simplifying
3x(x + -70) = 5

Reorder the terms:
3x(-70 + x) = 5
(-70 * 3x + x * 3x) = 5
(-210x + 3x2) = 5

Solving
-210x + 3x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + -210x + 3x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -210x + 3x2 = 0

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

Divide each side by '3'.
-1.666666667 + -70x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -70x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -70x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -70x + x2 = 0 + 1.666666667
-70x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-70x + x2 = 1.666666667

The x term is -70x.  Take half its coefficient (-35).
Square it (1225) and add it to both sides.

Add '1225' to each side of the equation.
-70x + 1225 + x2 = 1.666666667 + 1225

Reorder the terms:
1225 + -70x + x2 = 1.666666667 + 1225

Combine like terms: 1.666666667 + 1225 = 1226.666666667
1225 + -70x + x2 = 1226.666666667

Factor a perfect square on the left side:
(x + -35)(x + -35) = 1226.666666667

Calculate the square root of the right side: 35.023801431

Break this problem into two subproblems by setting 
(x + -35) equal to 35.023801431 and -35.023801431.

Subproblem 1
x + -35 = 35.023801431

Simplifying
x + -35 = 35.023801431

Reorder the terms:
-35 + x = 35.023801431

Solving
-35 + x = 35.023801431

Solving for variable 'x'.

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

Add '35' to each side of the equation.
-35 + 35 + x = 35.023801431 + 35

Combine like terms: -35 + 35 = 0
0 + x = 35.023801431 + 35
x = 35.023801431 + 35

Combine like terms: 35.023801431 + 35 = 70.023801431
x = 70.023801431

Simplifying
x = 70.023801431

Subproblem 2
x + -35 = -35.023801431

Simplifying
x + -35 = -35.023801431

Reorder the terms:
-35 + x = -35.023801431

Solving
-35 + x = -35.023801431

Solving for variable 'x'.

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

Add '35' to each side of the equation.
-35 + 35 + x = -35.023801431 + 35

Combine like terms: -35 + 35 = 0
0 + x = -35.023801431 + 35
x = -35.023801431 + 35

Combine like terms: -35.023801431 + 35 = -0.023801431
x = -0.023801431

Simplifying
x = -0.023801431

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {70.023801431, -0.023801431}