Solve the nonlinear inequality.Express the solution using interv 2x^2+xgeqslant 6 square

To solve the nonlinear inequality , we first rewrite it in standard form: Next, we solve the corresponding quadratic equation to find the critical points. We can use the quadratic formula: For the quadratic equation , , , and . Plugging these values into the quadratic formula gives: This gives us two solutions: Now, we test the intervals determined by these critical points: \((-\infty, -2)\), \((-2, \frac{3}{2})\), and \((\frac{3}{2}, \infty)\).For \(x \in (-\infty, -2)\), choose : For \(x \in (-2, \frac{3}{2})\), choose : Therefore, the solution to the inequality is: