SOLUTION: Solve the equation. {{{3(n-1)^2+20=19(n-1)}}}

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Question 45774: Solve the equation.
3%28n-1%29%5E2%2B20=19%28n-1%29
Answer by atif.muhammad(135) About Me  (Show Source):
You can put this solution on YOUR website!
3(n-1)^2+20=19(n-1)
3(n-1)^2+20=19n-19
3(n^2 - 2n + 1) +20 = 19n - 19
3n^2 - 6n + 3 + 20 = 19n - 19
3n^2 - 25n + 42 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-25x%2B42+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-25%29%5E2-4%2A3%2A42=121.

Discriminant d=121 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--25%2B-sqrt%28+121+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-25%29%2Bsqrt%28+121+%29%29%2F2%5C3+=+6
x%5B2%5D+=+%28-%28-25%29-sqrt%28+121+%29%29%2F2%5C3+=+2.33333333333333

Quadratic expression 3x%5E2%2B-25x%2B42 can be factored:
3x%5E2%2B-25x%2B42+=+3%28x-6%29%2A%28x-2.33333333333333%29
Again, the answer is: 6, 2.33333333333333. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-25%2Ax%2B42+%29