Factor completely 8xsquared minus 6x-9

Use quadratic formula to find roots of the equation 8x^{2}-6x-9=0.

x_{1,2}=[-(-6)±√((-6)^{2}-4*8*(-9))]/16; x_{1,2}=[6±√(36+288)]/16; x_{1}=-3/4; x_{2}=3/2

Thus, the trinomial 8x^{2}-6x-9 can be factored as follows: 8x^{2}-6x-9=8*(x+¾)*(x-3/2)=(4x+3)*(2x-3)