Explanation

Set t = √(3x²−7x−30) and u = √(2x²−7x−5). Then t² − u² = x² − 25 = (x−5)(x+5) while t − u = x−5, so dividing gives t + u = x + 5. Adding the two relations yields 2t = 2x, i.e. t = x, and squaring gives x² = 3x²−7x−30, or 2x²−7x−30 = 0. By Vieta's formulas the product of the roots is αβ = c/a = −30/2 = −15, which is option A.