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Since the highest exponent of x is 2, there will be two roots (although the roots might be complex, not real).
To find the roots, we want one side of the equation to be zero (which we already have) and then factor the other side. (Since this is a quadratic equation we we have option of using the Quadratic Formula. It is harder to use but it has the advantage of being able to find complex roots. Since we are only interested in real roots, we'll stick to factoring.
The GCF is 1 so we won't bother factoring it out. The left side is a difference of squares, , so it will factor according to that pattern: .
(4x+1)(4x-1) = 0
From the Zero Product Property we know that one of these factors must be zero. So:
4x+1 = 0 or 4x-1 = 0
Solving each of these we get:
x = -1/4 or x = 1/4
These are the two real roots for your equation.
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