SOLUTION: Solve 6y^2+5y-14=0 thank you

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Question 242824: Solve
6y^2+5y-14=0
thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

6y%5E2%2B5y-14=0 Start with the given equation.


Notice that the quadratic 6y%5E2%2B5y-14 is in the form of Ay%5E2%2BBy%2BC where A=6, B=5, and C=-14


Let's use the quadratic formula to solve for "y":


y+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


y+=+%28-%285%29+%2B-+sqrt%28+%285%29%5E2-4%286%29%28-14%29+%29%29%2F%282%286%29%29 Plug in A=6, B=5, and C=-14


y+=+%28-5+%2B-+sqrt%28+25-4%286%29%28-14%29+%29%29%2F%282%286%29%29 Square 5 to get 25.


y+=+%28-5+%2B-+sqrt%28+25--336+%29%29%2F%282%286%29%29 Multiply 4%286%29%28-14%29 to get -336


y+=+%28-5+%2B-+sqrt%28+25%2B336+%29%29%2F%282%286%29%29 Rewrite sqrt%2825--336%29 as sqrt%2825%2B336%29


y+=+%28-5+%2B-+sqrt%28+361+%29%29%2F%282%286%29%29 Add 25 to 336 to get 361


y+=+%28-5+%2B-+sqrt%28+361+%29%29%2F%2812%29 Multiply 2 and 6 to get 12.


y+=+%28-5+%2B-+19%29%2F%2812%29 Take the square root of 361 to get 19.


y+=+%28-5+%2B+19%29%2F%2812%29 or y+=+%28-5+-+19%29%2F%2812%29 Break up the expression.


y+=+%2814%29%2F%2812%29 or y+=++%28-24%29%2F%2812%29 Combine like terms.


y+=+7%2F6 or y+=+-2 Simplify.


So the solutions are y+=+7%2F6 or y+=+-2