4x^2+3x-270=0

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Solution for 4x^2+3x-270=0 equation: 


Simplifying
4x2 + 3x + -270 = 0

Reorder the terms:
-270 + 3x + 4x2 = 0

Solving
-270 + 3x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-67.5 + 0.75x + x2 = 0

Move the constant term to the right:

Add '67.5' to each side of the equation.
-67.5 + 0.75x + 67.5 + x2 = 0 + 67.5

Reorder the terms:
-67.5 + 67.5 + 0.75x + x2 = 0 + 67.5

Combine like terms: -67.5 + 67.5 = 0.0
0.0 + 0.75x + x2 = 0 + 67.5
0.75x + x2 = 0 + 67.5

Combine like terms: 0 + 67.5 = 67.5
0.75x + x2 = 67.5

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 67.5 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 67.5 + 0.140625

Combine like terms: 67.5 + 0.140625 = 67.640625
0.140625 + 0.75x + x2 = 67.640625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 67.640625

Calculate the square root of the right side: 8.224392075

Break this problem into two subproblems by setting 
(x + 0.375) equal to 8.224392075 and -8.224392075.


Subproblem 1
x + 0.375 = 8.224392075

Simplifying
x + 0.375 = 8.224392075

Reorder the terms:
0.375 + x = 8.224392075

Solving
0.375 + x = 8.224392075

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = 8.224392075 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 8.224392075 + -0.375
x = 8.224392075 + -0.375

Combine like terms: 8.224392075 + -0.375 = 7.849392075
x = 7.849392075

Simplifying
x = 7.849392075


Subproblem 2
x + 0.375 = -8.224392075

Simplifying
x + 0.375 = -8.224392075

Reorder the terms:
0.375 + x = -8.224392075

Solving
0.375 + x = -8.224392075

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = -8.224392075 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -8.224392075 + -0.375
x = -8.224392075 + -0.375

Combine like terms: -8.224392075 + -0.375 = -8.599392075
x = -8.599392075

Simplifying
x = -8.599392075


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.849392075, -8.599392075}

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