SOLUTION: 3x^2+13x-10=0

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Question 775290: 3x^2+13x-10=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2%2B13x-10=0 Start with the given equation.


Notice that the quadratic 3x%5E2%2B13x-10 is in the form of Ax%5E2%2BBx%2BC where A=3, B=13, 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-%2813%29+%2B-+sqrt%28+%2813%29%5E2-4%283%29%28-10%29+%29%29%2F%282%283%29%29 Plug in A=3, B=13, and C=-10


x+=+%28-13+%2B-+sqrt%28+169-4%283%29%28-10%29+%29%29%2F%282%283%29%29 Square 13 to get 169.


x+=+%28-13+%2B-+sqrt%28+169--120+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-10%29 to get -120


x+=+%28-13+%2B-+sqrt%28+169%2B120+%29%29%2F%282%283%29%29 Rewrite sqrt%28169--120%29 as sqrt%28169%2B120%29


x+=+%28-13+%2B-+sqrt%28+289+%29%29%2F%282%283%29%29 Add 169 to 120 to get 289


x+=+%28-13+%2B-+sqrt%28+289+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%28-13+%2B-+17%29%2F%286%29 Take the square root of 289 to get 17.


x+=+%28-13+%2B+17%29%2F%286%29 or x+=+%28-13+-+17%29%2F%286%29 Break up the expression.


x+=+%284%29%2F%286%29 or x+=++%28-30%29%2F%286%29 Combine like terms.


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


So the solutions are x+=+2%2F3 or x+=+-5