30x^2+45x-9750=0

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Solution for 30x^2+45x-9750=0 equation: 


Simplifying
30x2 + 45x + -9750 = 0

Reorder the terms:
-9750 + 45x + 30x2 = 0

Solving
-9750 + 45x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '15'.
15(-650 + 3x + 2x2) = 0

Ignore the factor 15.

Subproblem 1
Set the factor '(-650 + 3x + 2x2)' equal to zero and attempt to solve:

Simplifying
-650 + 3x + 2x2 = 0

Solving
-650 + 3x + 2x2 = 0

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

Divide each side by '2'.
-325 + 1.5x + x2 = 0

Move the constant term to the right:

Add '325' to each side of the equation.
-325 + 1.5x + 325 + x2 = 0 + 325

Reorder the terms:
-325 + 325 + 1.5x + x2 = 0 + 325

Combine like terms: -325 + 325 = 0
0 + 1.5x + x2 = 0 + 325
1.5x + x2 = 0 + 325

Combine like terms: 0 + 325 = 325
1.5x + x2 = 325

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 325 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 325 + 0.5625

Combine like terms: 325 + 0.5625 = 325.5625
0.5625 + 1.5x + x2 = 325.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 325.5625

Calculate the square root of the right side: 18.043350576

Break this problem into two subproblems by setting 
(x + 0.75) equal to 18.043350576 and -18.043350576.


Subproblem 1
x + 0.75 = 18.043350576

Simplifying
x + 0.75 = 18.043350576

Reorder the terms:
0.75 + x = 18.043350576

Solving
0.75 + x = 18.043350576

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 18.043350576 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 18.043350576 + -0.75
x = 18.043350576 + -0.75

Combine like terms: 18.043350576 + -0.75 = 17.293350576
x = 17.293350576

Simplifying
x = 17.293350576


Subproblem 2
x + 0.75 = -18.043350576

Simplifying
x + 0.75 = -18.043350576

Reorder the terms:
0.75 + x = -18.043350576

Solving
0.75 + x = -18.043350576

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -18.043350576 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -18.043350576 + -0.75
x = -18.043350576 + -0.75

Combine like terms: -18.043350576 + -0.75 = -18.793350576
x = -18.793350576

Simplifying
x = -18.793350576


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.293350576, -18.793350576}
Solution
x = {17.293350576, -18.793350576}

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