SOLUTION: Please help me solve: -3x^2 + 75x=125+6x

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Question 420637: Please help me solve: -3x^2 + 75x=125+6x
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
-3x%5E2+%2B+75x=125%2B6x
Because of the squared term this is a quadratic equation. To solve a quadratic equation we want one side to be zero. And since the rest of the problem will be easier if the squared term has a positive coefficient, I am going to subtract the entire left side from both sides of the equation:
0+=+3x%5E2+-+69x+%2B+125
This equation does not factor so we will use the Quadratic Formula:
x+=+%28-%28-69%29+%2B-+sqrt%28%28-69%29%5E2+-+4%283%29%28125%29%29%29%2F2%283%29
which simplifies as follows:
x+=+%28-%28-69%29+%2B-+sqrt%284761+-+4%283%29%28125%29%29%29%2F2%283%29
x+=+%28-%28-69%29+%2B-+sqrt%284761+-+1500%29%29%2F2%283%29
x+=+%28-%28-69%29+%2B-+sqrt%283261%29%29%2F2%283%29
x+=+%2869+%2B-+sqrt%283261%29%29%2F6
There are no perfect square factors in 3261 so the square root will not simplify. The solutions to your equation are:
x+=+%2869+%2B+sqrt%283261%29%29%2F6 or x+=+%2869+-+sqrt%283261%29%29%2F6