Решить квадратные уравнения: (через дискриминант)

1) 6x^2-12=0
2) 3a^2+5a+2=0
3) 4x+4x^2+1=0
4) 3x^2+7x-6=0
5) 5x^2-22x-15=0
6) 3x^2-10x+9=0

1) 6x^2 - 12 = 0

6(x^2 - 2) = 0

x^2 = 2

x = ±√2

2)  3a^2 + 5a + 2 = 0

D = b^2 - 4ac = 25 - 4 * 3 * 2 = 25 - 24 = 1, √D = 1.

a1 = (-5 + 1) / 6 = -4/6 = -2/3

a2 = (-5 - 1) / 6 = -1

3) 4x + 4x^2 + 1 = 0

4x^2 + 4x + 1 = 0

D = k^2 - ac (вторая формула для нахождения дискр.) = 2^2 - 4*1 = 0

x1 = -2 + 0 / 4 = -0,5

4) 3x^2 + 7x - 6 = 0

D = b^2 - 4ac = 49 - 4 * 3 * (-6) = 49 +72 = 121, √D = 11

x1 = -7 + 11 / 6 = 4/6 = 2/3

x2 = -7 - 11 / 6 = -3

5) 5x^2 - 22x - 15 = 0

D = k^2 - ac = 11^2 - 5 * (-15) = 121 + 75 = 196, √D = 14

x1 = 11 + 14 / 5 = 25 / 5 = 5

x2 = 11 - 14 / 5 = -3/5 = - 0,6

6) 3x^2 - 10x + 9 = 0

D = k^2 - ac = 25 - 3 * 9 = 25 - 27 = -2, √D < 0, корней нет.