SOLUTION: 4y^2-7y-15=0

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Question 236208: 4y^2-7y-15=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4y%5E2-7y-15=0 Start with the given equation.


Notice that the quadratic 4y%5E2-7y-15 is in the form of Ay%5E2%2BBy%2BC where A=4, B=-7, and C=-15


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-%28-7%29+%2B-+sqrt%28+%28-7%29%5E2-4%284%29%28-15%29+%29%29%2F%282%284%29%29 Plug in A=4, B=-7, and C=-15


y+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%284%29%28-15%29+%29%29%2F%282%284%29%29 Negate -7 to get 7.


y+=+%287+%2B-+sqrt%28+49-4%284%29%28-15%29+%29%29%2F%282%284%29%29 Square -7 to get 49.


y+=+%287+%2B-+sqrt%28+49--240+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-15%29 to get -240


y+=+%287+%2B-+sqrt%28+49%2B240+%29%29%2F%282%284%29%29 Rewrite sqrt%2849--240%29 as sqrt%2849%2B240%29


y+=+%287+%2B-+sqrt%28+289+%29%29%2F%282%284%29%29 Add 49 to 240 to get 289


y+=+%287+%2B-+sqrt%28+289+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


y+=+%287+%2B-+17%29%2F%288%29 Take the square root of 289 to get 17.


y+=+%287+%2B+17%29%2F%288%29 or y+=+%287+-+17%29%2F%288%29 Break up the expression.


y+=+%2824%29%2F%288%29 or y+=++%28-10%29%2F%288%29 Combine like terms.


y+=+3 or y+=+-5%2F4 Simplify.


So the solutions are y+=+3 or y+=+-5%2F4