Решите уравнения:

1) 2x (5x-7) = 2x^2-5

2) (x+4) ^2=4x^2+5

3) (x-5) ^2=3x^2-x+14

4) 9x (4x-1) = 3x-1

1) 2x (5x-7) = 2x^2-5

10x^2-14x-2x^2+5=0

8x^2-14x+5=0

D = (-14) ^2-4*8*5=196-160=36

x1=14+6/16=20/16=5/4=1,25

x2=14-6/16=8/16=1/2=0,5

2) (x+4) ^2=4x^2+5

x^2+8x+16-4x^2-5=0

-3x^2+8x+11=0 * (-1)

3x^2-8x-11=0

D = (-8) ^2-4*3 * (-11) = 64+132=196

x1=8+14/6=22/6=11/3=3 2/3

x2=8-14/6=-6/6=-1

3) (x-5) ^2=3x^2-x+14

x^2-10x+25-3x^2+x-14=0

-2x^2-9x+11=0 * (-1)

2x^2+9x-11=0

D=9^2-4*2 * (-11) = 81+88=169

x1=-9+13/4=4/4=1

x2=-9-13/4=-22/4=5,5

4) 9x (4x-1) = 3x-1

36x^2-9x-3x+1=0

36x^2-12x+1=0

D = (-12) ^2-4*36*1=144-144=0

x1=12+0/72=1/6

x2=12-0/72=1/6