SOLUTION: Please help me solve this equation: {{{ 3*x^2-16*x+5=0 }}}

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Question 195129: Please help me solve this equation: +3%2Ax%5E2-16%2Ax%2B5=0+
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2-16x%2B5=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc=0 where a=3, b=-16, and c=5


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-%28-16%29+%2B-+sqrt%28+%28-16%29%5E2-4%283%29%285%29+%29%29%2F%282%283%29%29 Plug in a=3, b=-16, and c=5


x+=+%2816+%2B-+sqrt%28+%28-16%29%5E2-4%283%29%285%29+%29%29%2F%282%283%29%29 Negate -16 to get 16.


x+=+%2816+%2B-+sqrt%28+256-4%283%29%285%29+%29%29%2F%282%283%29%29 Square -16 to get 256.


x+=+%2816+%2B-+sqrt%28+256-60+%29%29%2F%282%283%29%29 Multiply 4%283%29%285%29 to get 60


x+=+%2816+%2B-+sqrt%28+196+%29%29%2F%282%283%29%29 Subtract 60 from 256 to get 196


x+=+%2816+%2B-+sqrt%28+196+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%2816+%2B-+14%29%2F%286%29 Take the square root of 196 to get 14.


x+=+%2816+%2B+14%29%2F%286%29 or x+=+%2816+-+14%29%2F%286%29 Break up the expression.


x+=+%2830%29%2F%286%29 or x+=++%282%29%2F%286%29 Combine like terms.


x+=+5 or x+=+1%2F3 Simplify.


So the solutions are x+=+5 or x+=+1%2F3