<s>[INST] Finding the sum of real solutions to an equation how to find the sum of real solutions 
if,
$(x+1)(x+\frac14)(x+\frac12)(x+\frac34)=\frac{45}{32}$
I have tried multiplying both sides with 32 and got
$\frac{1}{32}(x+1)(2x+1)(4x+1)(4x+3)=\frac{45}{32}$
then i multiplied and got
$\frac{1}{32}(32x^4+80x^3+70x^2+25x+3)=\frac{45}{32}$
which is equal to
$32x^4+80x^3+70x^2+25x+3=45$
and
$32x^4+80x^3+70x^2+25x-42=0$
but i couldn't come up with something else...
Any help is appreciated!
 [/INST] This is a fine start. Now you should know something about the sum of roots of a polynomial, right ? In case you don't: write your polynomial
$ x^4 + 5/2 x^2 + 35/16 x^2 + 25/32 x - 21/16 = 0$ as $(x-a)(x-b)(x-c)(x-d)$. Expand the right-hand side. What can you identify with $a+b+c+d$ ?
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