Solve for .

Rearranging  a little, we have...

4x^2 - 7x - 2 = 0

And factoring produces

(4x + 1 ) (x - 2) = 0

And setting each factor to 0, we obtain that

x = -1/4  and   x  =  2   as Aziz has said...

4x^2 - 7x - 2 = 0

Use the quadratic formula: x = (7 +/- sqrt[49 - 4(4)(-2)]) / 2(4) -->

(7 +/- sqrt(49 + 32)) / 8 -->

(7 +/- sqrt(81)) / 8 -->

(7 +/- 9) / 8 -->

x = (7 + 9) / 8 = 16 / 8 = 2

&

x = (7 - 9) / 8 = -2 / 8 = -1/4 = -0.25

Note: 4(2^2) -2 ?= 7(2) --> 16 - 2 = 14 --> Yes, therefore, x = 2 is a solution.

4((-1/4)^2) - 2 ?= 7(-1/4) --> -1.75 ?= -1.75 --> Yes, therefore, x = -1/4 is a solution, too.