2.3 Solve fine \( x ; \) \( 2.3 .1 \quad \frac{x(x-5)}{6}-1=0 \) \( 2.3 .2 \quad e=\sqrt{a+2 x} \) 2.4 Tabelo is currently four times as old as his dalghter. Linda, Six years from now Tabelo will be three times as old as Linda. Calculate Linda'a ago currently.

### 2.3.1 Solve the equation \[ \frac{x(x-5)}{6} - 1 = 0. \] **Step 1.** Multiply both sides by \(6\) to eliminate the fraction: \[ x(x-5) - 6 = 0. \] **Step 2.** Expand the left-hand side: \[ x^2 - 5x - 6 = 0. \] **Step 3.** Factor the quadratic equation: \[ (x - 6)(x + 1) = 0. \] **Step 4.** Set each factor equal to zero: \[ x - 6 = 0 \quad \text{or} \quad x + 1 = 0, \] which gives \[ x = 6 \quad \text{or} \quad x = -1. \] --- ### 2.3.2 Solve for \( x \) in the equation \[ e = \sqrt{a + 2x}. \] **Step 1.** Square both sides to eliminate the square root: \[ e^2 = a + 2x. \] **Step 2.** Solve for \( x \): \[ 2x = e^2 - a, \] \[ x = \frac{e^2 - a}{2}. \] --- ### 2.4 Tabelo is currently four times as old as his daughter Linda. Six years from now Tabelo will be three times as old as Linda. To find Linda's current age, let \( L \) be Linda's age now and \( T \) be Tabelo's age now. **Step 1.** Write the relationship between their current ages: \[ T = 4L. \] **Step 2.** Write the relationship for their ages after six years: \[ T + 6 = 3(L + 6). \] **Step 3.** Substitute \( T = 4L \) into the second equation: \[ 4L + 6 = 3(L + 6). \] **Step 4.** Expand the right-hand side: \[ 4L + 6 = 3L + 18. \] **Step 5.** Solve for \( L \): \[ 4L - 3L = 18 - 6, \] \[ L = 12. \] Linda is currently \(12\) years old.