[tex]7x(x - 2)(9 - 3x) = 0[/tex]
[tex]7x(9x - 3 {x}^{2} - 18 + 6x) = 0[/tex]
[tex]63 {x}^{2} - 21 {x}^{3} - 126x + 42 {x}^{2} = 0[/tex]
[tex] - 21 {x}^{3} + 105 {x}^{2} - 126x = 0 | \times ( - 1)[/tex]
[tex]21 {x}^{3} - 105 {x}^{2} + 126x = 0[/tex]
[tex] - 21x( - {x}^{2} + 5x - 6) = 0[/tex]
[tex] - 21x = 0 | \div ( - 21) \\ x = 0[/tex]
[tex] - {x}^{2} + 5x - 6 = 0[/tex]
[tex]a = - 1 \\ b = 5 \\ c = - 6[/tex]
∆=
[tex] {b}^{2} - 4ac = {5}^{2} - 4 \times ( - 1) \times ( - 6) = 25 - 24 = 1[/tex]
√∆=1
[tex] x_{1} = \frac{ - b - \sqrt{delty} }{2a} = \frac{ - 5 - 1}{2 \times ( - 1)} = \frac{ - 6}{ - 2} = 3[/tex]
[tex] x_{2} = \frac{ - b + \sqrt{delty} }{2a} = \frac{ - 5 + 1}{2 \times ( - 1)} = \frac{ - 4}{ - 2} = 2[/tex]
Odp. Równanie ma 3 rozwiązania:
[tex]x = 0 \\ x = 2 \\ x = 3[/tex]
