a) 12x^2+36x=0
12x(x+3) = 0
12x = 0
x = 0
и
x + 3 = 0
x = -3
Ответ : 0; -3
б)
2x^2 - 7x - 15 = 0
Штучный способ :
2x^2/2 - 7x - 15*2 = 0
x -> a
a^2 - 7a - 30 = 0
a1 = 10
a2 = -3
x1 = 10/2 = 5;
x2 = -3/2 = -1,5
Ответ : 5; -1,5;
Через дискриминант :
2x^2 - 7x - 15 = 0
a=2; b=-7; c=-15
D = b^2 - 4ac = (-7)^2 - 4 * 2 * (-15) = 49 + 120 = 169 = 13^2
D>0
x1 = -b + √D/2a = 7 + 13/2*2 = 20/4 = 5;
x2 = -b - √D/2a = 7 - 13/2*2 = -6/4 = -3/2 = -1,5;
Ответ : 5; -1,5;