Solve this equation. x^3 - 4x^2 + 6x - 24 = 0

To solve this cub ic equation , we can use the quadratic formula or complete the square method . Here , we will use the quadratic formula : \n \n x = (- b ± √ ( b ^ 2 - 4 ac )) / 2 a \n \n In this case , a = 1 , b = - 4 , and c = 6 . Pl ug ging these values into the formula , we get : \n \n x = (- (- 4 ) ± √ (( - 4 )^ 2 - 4 \ * 1 \ * 6 )) / 2 \ * 1 \n \n x = ( 4 ± √ ( 1 6 + 2 4 )) / 2 \n \n x = ( 4 ± √ 3 6 ) / 2 \n \n x = ( 4 ± 6 ) / 2 \n \n x = ( 2 ± 1 2 ) / 2 \n \n x = ( 2 ± 6 ) / 2 \n \n x = ( 8 / 2 ) or ( 1 4 / 2 ) \n \n So , the solutions to the given cub ic equation are x = 4 and x = 1 4 . </s>