SOLUTION: what is the solution to 3x^2=8x+9 ?

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Question 210914: what is the solution to 3x^2=8x+9 ?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2=8x%2B9 Start with the given equation.


3x%5E2-8x-9=0 Get every term to the left side.


Notice that the quadratic 3x%5E2-8x-9 is in the form of Ax%5E2%2BBx%2BC where A=3, B=-8, and C=-9


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-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%283%29%28-9%29+%29%29%2F%282%283%29%29 Plug in A=3, B=-8, and C=-9


x+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%283%29%28-9%29+%29%29%2F%282%283%29%29 Negate -8 to get 8.


x+=+%288+%2B-+sqrt%28+64-4%283%29%28-9%29+%29%29%2F%282%283%29%29 Square -8 to get 64.


x+=+%288+%2B-+sqrt%28+64--108+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-9%29 to get -108


x+=+%288+%2B-+sqrt%28+64%2B108+%29%29%2F%282%283%29%29 Rewrite sqrt%2864--108%29 as sqrt%2864%2B108%29


x+=+%288+%2B-+sqrt%28+172+%29%29%2F%282%283%29%29 Add 64 to 108 to get 172


x+=+%288+%2B-+sqrt%28+172+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%288+%2B-+2%2Asqrt%2843%29%29%2F%286%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%288%2B2%2Asqrt%2843%29%29%2F%286%29 or x+=+%288-2%2Asqrt%2843%29%29%2F%286%29 Break up the expression.


x+=+%284%2Bsqrt%2843%29%29%2F%283%29 or x+=+%284-sqrt%2843%29%29%2F%283%29 Reduce


So the solutions are x+=+%284%2Bsqrt%2843%29%29%2F%283%29 or x+=+%284-sqrt%2843%29%29%2F%283%29