1. What is the negative solution to this equation? 8x^2-4x=24

Rearrange the equation:<br />$8x^2 - 4x - 24 = 0$<br />Factorize the equation:<br />$4(2x^2 - x - 6) = 0$<br />Further factorize:<br />$4(2x + 3)(x - 2) = 0$<br />Set each factor to zero and solve for $x$:<br />$2x + 3 = 0$ or $x - 2 = 0$<br />Solve for $x$:<br />$x_1 = -\frac{3}{2}$, $x_2 = 2$<br />The negative solution is $x_1 = -\frac{3}{2}$.