how would i solve 10xsquared-3x-1=0

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you would first have to factor it and it would break down to (5x+1)(2x-1)=0. To check you can always use foil and you will know you are right if you get the orginal answer. Now you have to equations, 5x+1=0 and 2x-1=0, so you solve them normally.  5x+1=05x=-1x=-1/5 and 2x-1=02x=1x=1/2  x=1/2 an x=-1/5 are your final answers