Ответ:

1) 12x-35-x²=0

-x²+12x-35=0

D= 12²-4*35= 144-140= 4= 2²

x₁= (12+2)/2= 14/2= 7

x₂= (12-2)/2= 10/2= 5

2) x²-11x-42=0

D=(-11)²+ 4*42= 121+168= 289= 17²

x₁= -(11-17)/2= -6/2= -3

x₂= -(11+17)/2= -28/2= -14

3) 2+3x²-4x=0

3x²-4x+2=0

D=(-4)²- 4*3*2= 16-24= -8

Нет корней, т.к. D<0

4) -24x-9-16x²=0

-16x²-24x-9=0

D=(-24)²-4*16*9= 576-576=0

x₀= -24/32= -0.75

5) 5x-x²= 0

-x²+5x=0

D=5²+4*0= 25= 5²

x₁= (5+5)/2=10/2= 5

x₂= (5-5)/2 = 0/2=0

6) -x²+8=0

D= 0²+4*8= 32= √32

x₁=(√32)/2= (4√2)/2= 2√2

x₂=-(√32)/2= -(4√2)/2= -2√2

7) 17a-12-6a²=0

-6a²+17a-12=0

D=17²-4*6*12= 289-288=1=1²

a₁= -(17-1)/12= -16/12= -8/2

a₂= -(17+1)/12= -18/12= -3/2

Объяснение: