Solve for \( x \). Enter the solutions from least to greatest. \( 6 x^{2}-30 x-84=0 \) lesser \( x=\square \) greater \( x=\square \)

To solve the quadratic equation \( 6x^{2} - 30x - 84 = 0 \), we can start by simplifying the equation. First, we can divide all terms by 6: \[ x^{2} - 5x - 14 = 0 \] Now we can factor the equation. We look for two numbers that multiply to \(-14\) and add up to \(-5\). These numbers are \(-7\) and \(2\): \[ (x - 7)(x + 2) = 0 \] Setting each factor to zero gives us the solutions: 1. \( x - 7 = 0 \) → \( x = 7 \) 2. \( x + 2 = 0 \) → \( x = -2 \) So the solutions from least to greatest are: lesser \( x = -2 \) greater \( x = 7 \)