SOLUTION: solve 3x^2-7x-6=0

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Question 210159: solve 3x^2-7x-6=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2-7x-6=0 Start with the given equation.


Notice that the quadratic 3x%5E2-7x-6 is in the form of Ax%5E2%2BBx%2BC where A=3, B=-7, and C=-6


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-%28-7%29+%2B-+sqrt%28+%28-7%29%5E2-4%283%29%28-6%29+%29%29%2F%282%283%29%29 Plug in A=3, B=-7, and C=-6


x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%283%29%28-6%29+%29%29%2F%282%283%29%29 Negate -7 to get 7.


x+=+%287+%2B-+sqrt%28+49-4%283%29%28-6%29+%29%29%2F%282%283%29%29 Square -7 to get 49.


x+=+%287+%2B-+sqrt%28+49--72+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-6%29 to get -72


x+=+%287+%2B-+sqrt%28+49%2B72+%29%29%2F%282%283%29%29 Rewrite sqrt%2849--72%29 as sqrt%2849%2B72%29


x+=+%287+%2B-+sqrt%28+121+%29%29%2F%282%283%29%29 Add 49 to 72 to get 121


x+=+%287+%2B-+sqrt%28+121+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%287+%2B-+11%29%2F%286%29 Take the square root of 121 to get 11.


x+=+%287+%2B+11%29%2F%286%29 or x+=+%287+-+11%29%2F%286%29 Break up the expression.


x+=+%2818%29%2F%286%29 or x+=++%28-4%29%2F%286%29 Combine like terms.


x+=+3 or x+=+-2%2F3 Simplify.


So the solutions are x+=+3 or x+=+-2%2F3