а) 6x²-x=0, б) - 9+4x²=0, в) 12x²+7x+1=0, г) 3x²+5x+6=0

а)

6x^2 - x = 0; x (6x - 1) = 0; [x = 0;

[6x - 1 = 0; [x = 0;

[6x = 1; [x = 0;

[x = 1/6.

б)

-9 + 4x^2 = 0; (2x) ^2 - 3^2 = 0; (2x + 3) (2x - 3) = 0; [2x + 3 = 0;

[2x - 3 = 0; [2x = - 3;

[2x = 3; [x = - 3/2;

[x = 3/2; [x = - 1,5;

[x = 1,5.

в)

12x^2 + 7x + 1 = 0; D = 7^2 - 4 * 12 * 1 = 49 - 48 = 1; x = (-7 ± √1) / (2 * 12) = (-7 ± 1) / 24; x1 = (-7 - 1) / 24 = - 8/24 = - 1/3; x2 = (-7 + 1) / 24 = - 6/24 = - 1/4;

г)

3x^2 + 5x + 6 = 0; D = 5^2 - 4 * 3 * 6 = 25 - 72 = - 47 < 0 - нет решений.

Ответ: а) 0; 1/6; б) - 1,5; 1,5; в) - 1/3; - 1/4; г) нет решений.