\( 1.1 .1 \quad x(6 x-5)=6 \)

To solve the equation \( x(6x - 5) = 6 \), let's first expand it: \[ 6x^2 - 5x = 6. \] Next, we rearrange it to form a standard quadratic equation: \[ 6x^2 - 5x - 6 = 0. \] Now we can apply the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 6 \), \( b = -5 \), and \( c = -6 \). Plugging in these values gives: \[ b^2 - 4ac = (-5)^2 - 4(6)(-6) = 25 + 144 = 169. \] Thus, the solutions are: \[ x = \frac{5 \pm \sqrt{169}}{12} = \frac{5 \pm 13}{12}. \] Calculating these, we get the solutions: 1. \( x = \frac{18}{12} = \frac{3}{2} \) 2. \( x = \frac{-8}{12} = -\frac{2}{3} \) Therefore, the solutions are \( x = \frac{3}{2} \) and \( x = -\frac{2}{3} \).