SOLUTION: Solve and show steps using the quadratic formula: 3x^2-2x=15x-10

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Question 184186: Solve and show steps using the quadratic formula:
3x^2-2x=15x-10
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2-2x=15x-10 Start with the given equation.


3x%5E2-2x-15x%2B10=0 Get all terms to the left side.


3x%5E2-17x%2B10=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=3, b=-17, and c=10


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-17%29+%2B-+sqrt%28+%28-17%29%5E2-4%283%29%2810%29+%29%29%2F%282%283%29%29 Plug in a=3, b=-17, and c=10


x+=+%2817+%2B-+sqrt%28+%28-17%29%5E2-4%283%29%2810%29+%29%29%2F%282%283%29%29 Negate -17 to get 17.


x+=+%2817+%2B-+sqrt%28+289-4%283%29%2810%29+%29%29%2F%282%283%29%29 Square -17 to get 289.


x+=+%2817+%2B-+sqrt%28+289-120+%29%29%2F%282%283%29%29 Multiply 4%283%29%2810%29 to get 120


x+=+%2817+%2B-+sqrt%28+169+%29%29%2F%282%283%29%29 Subtract 120 from 289 to get 169


x+=+%2817+%2B-+sqrt%28+169+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%2817+%2B-+13%29%2F%286%29 Take the square root of 169 to get 13.


x+=+%2817+%2B+13%29%2F%286%29 or x+=+%2817+-+13%29%2F%286%29 Break up the expression.


x+=+%2830%29%2F%286%29 or x+=++%284%29%2F%286%29 Combine like terms.


x+=+5 or x+=+2%2F3 Simplify.


So the answers are x+=+5 or x+=+2%2F3