3х²-12=0
3х²=12|÷3
х²=4
х1=-2
х2=2
2х²+10х=0
2х(х+5)=0
2х=0|÷2
х=0
х+5=0
х=-5
х1=0
х2=-5
2х²-7х+3=0
D=(-(-7))²-4×2×3=49-24=25
x1=(-(-7)-√25)/2×2=(7-5)/4=2/4=1/2=0,5
x2=(-(-7)+√25)/2×2=(7+5)/4=12/4=3
x1=0,5
x2=3
3x²-x-14=0
D=(-(-1))²-4×3×(-14)=1+168=169
x1=(-(-1)-√169)/2×3=(1-13)/6=12/6=2
x2=(-(-1)+√169)/2×3=(1+13)/6=14/6=2(4/6)=2⅔
x1=2
x2=2⅔
⅔x²-2(5/6)x=½x+4
⅔x²-2(5/6)x-½x-4=0|×6
4x²-17x-3x-24=0
4x²-20x-24=0|÷4
x²-5x-6=0
По теореме Виета:
х1+х2=-(-5)=5
х1×х2=-6
х1=-1
х2=6
3х²-12=0
3х²=12|÷3
х²=4
х1=-2
х2=2
2х²+10х=0
2х(х+5)=0
2х=0|÷2
х=0
х+5=0
х=-5
х1=0
х2=-5
2х²-7х+3=0
D=(-(-7))²-4×2×3=49-24=25
x1=(-(-7)-√25)/2×2=(7-5)/4=2/4=1/2=0,5
x2=(-(-7)+√25)/2×2=(7+5)/4=12/4=3
x1=0,5
x2=3
3x²-x-14=0
D=(-(-1))²-4×3×(-14)=1+168=169
x1=(-(-1)-√169)/2×3=(1-13)/6=12/6=2
x2=(-(-1)+√169)/2×3=(1+13)/6=14/6=2(4/6)=2⅔
x1=2
x2=2⅔
⅔x²-2(5/6)x=½x+4
⅔x²-2(5/6)x-½x-4=0|×6
4x²-17x-3x-24=0
4x²-20x-24=0|÷4
x²-5x-6=0
По теореме Виета:
х1+х2=-(-5)=5
х1×х2=-6
х1=-1
х2=6