SOLUTION: solve the equation 5/2x-3 = 2x/x+4 please help me solve this equation

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Question 197267: solve the equation
5/2x-3 = 2x/x+4
please help me solve this equation
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5%2F%282x-3%29=%282x%29%2F%28x%2B4%29 Start with the given equation.


5%28x%2B4%29=2x%282x-3%29 Cross multiply


5x%2B20=4x%5E2-6x Distribute


0=4x%5E2-6x-5x-20 Get all terms to the right side


0=4x%5E2-11x-20 Combine like terms.


Notice we have a quadratic in the form of Ax%5E2%2BBx%2BC where A=4, B=-11, and C=-20


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-%28-11%29+%2B-+sqrt%28+%28-11%29%5E2-4%284%29%28-20%29+%29%29%2F%282%284%29%29 Plug in A=4, B=-11, and C=-20


x+=+%2811+%2B-+sqrt%28+%28-11%29%5E2-4%284%29%28-20%29+%29%29%2F%282%284%29%29 Negate -11 to get 11.


x+=+%2811+%2B-+sqrt%28+121-4%284%29%28-20%29+%29%29%2F%282%284%29%29 Square -11 to get 121.


x+=+%2811+%2B-+sqrt%28+121--320+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-20%29 to get -320


x+=+%2811+%2B-+sqrt%28+121%2B320+%29%29%2F%282%284%29%29 Rewrite sqrt%28121--320%29 as sqrt%28121%2B320%29


x+=+%2811+%2B-+sqrt%28+441+%29%29%2F%282%284%29%29 Add 121 to 320 to get 441


x+=+%2811+%2B-+sqrt%28+441+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%2811+%2B-+21%29%2F%288%29 Take the square root of 441 to get 21.


x+=+%2811+%2B+21%29%2F%288%29 or x+=+%2811+-+21%29%2F%288%29 Break up the expression.


x+=+%2832%29%2F%288%29 or x+=++%28-10%29%2F%288%29 Combine like terms.


x+=+4 or x+=+-5%2F4 Simplify.


So the solutions are x+=+4 or x+=+-5%2F4