d)
\frac{2}{x}=\frac{3x+3}{1-7x}
x\ne 0 , x\ne \frac{1}{7}
x(3x+3)=2(1-7x)
3x^2+3x=2-14x
3x^2+3x-2+14x=0
3x^2+17x-2=0
\Delta=17^2-4*3*(-2)=313
\sqrt\Delta=\sqrt{313}
x_1=\frac{-17-\sqrt{313}}{2*3}=\frac{-17-\sqrt{313}}{6}
x_2=\frac{-17+\sqrt{313}}{2*3}=\frac{\sqrt{313}-17}{6}
e)
\frac{3x-5}{x}=\frac{x}{4x+16}
x\ne0 i 4x+16\ne0 => 4x\ne-16 => x\ne 4
(3x-5)(4x+16)=x^2
12x^2+48x-20x-80-x^2=0
11x^2+28x-80=0
\Delta=28^2-4*11*(-80)=4304=16*269
\sqrt\Delta=\sqrt{16*269}=4\sqrt{269}
x_1=\frac{-28-4\sqrt{269}}{2*11}=\frac{2(-14-2\sqrt{269)}}{2*11}=\frac{-14-2\sqrt{269}}{11}
x_2=\frac{-28+4\sqrt{269}}{2*11}=\frac{2(2\sqrt{269}-14)}{2*11}=\frac{2\sqrt{269-14}}{11}
f)
\frac{5x^2-2x-2}{2-x}=\frac{x+4}{5}
x\ne 2
5(5x^2-2x-2)=(x+4)(2-x)
25x^2-10x-10=2x-x^2+8-4x
25x^2-10x-10-2x+x^2-8+4x=0
26x^2-8x-18=0 |:2
13x^2-4x-9=0
a=13, b=-4, c=-9
\Delta=(-4)^2-4*13*(-9)=16+468=484
\sqrt\Delta=22
x_1=\frac{4-22}{2*13}=\frac{-18}{26}=-\frac{9}{13}
x_2=\frac{4+22}{2*13}=\frac{26}{26}=1