Verified answer

1)

[tex]3 {x}^{2} - 0.9x = 0 \\ {x}^{2} - 0.3x = 0 \\ x(x - 0.3) = 0 \\ x_{1} = 0 \\ x _{2} = 0.3[/tex]

2)

[tex]4 {x}^{2} - 5x - 6 = 0 \\ d = ( - 5) {}^{2} - 4 \times 4 \times ( - 6) = \\ 25 + 96 = 121 \\ x_{1} = \frac{5 + 11}{4 \times 2} = \frac{16}{8} = 2 \\ x _{2} = \frac{5 - 11}{4 \times 2} = - \frac{6}{8} = - \frac{3}{4} = - 0.75[/tex]

3)

[tex] {x}^{2} + 14x + 33 = 0 \\ x_{1} + x _{2} = - 14 \\ x_{1} \times x _{2} = 33 \\ x_{1} = - 11 \\ x _{2} = - 3[/tex]

4)

[tex]4(x - 3) {}^{2} + 8x - 29 = 0 \\ 4( {x}^{2} - 6x + 9) + 8x - 29 = \\ 4x {}^{2} - 24x + 36 + 8x - 29 = 0 \\ 4 {x }^{2} - 16x + 7 = 0 \\ d = ( - 16) {}^{2} - 4 \times 4 \times 7 = \\ 256 - 112 = 144 \\ x_{1} = \frac{16 + 12}{2 \times 4} = \frac{28}{8} = \frac{7}{2} = 3.5 \\ x _{2} = \frac{16 - 12}{2 \times 4} = \frac{4}{2 \times 4} = \frac{1}{2} =0 .5[/tex]