a)
[tex]4x^2=12x-9\\4x^2-12x+9=0\\(2x-3)^2=0\\2x-3=0\\2x=3\ |:2\\x=\frac{3}{2}\\x=1\frac{1}{2}[/tex]
b)
[tex](2x-3)(2x+3)=(x+5)^2-9\\4x^2-9=x^2+10x+25-9\\3x^2-10x-25=0\\\Delta=(-10)^2-4*3*(-25)=100+300=400\\\sqrt\Delta=20\\x_1=\frac{10-20}{2*3}=\frac{-10}{6}=-\frac{5}{3}=-1\frac{2}{3}\\x_2=\frac{10+20}{2*3}=\frac{30}{6}=5\\x\in\{-1\frac{2}{3},5\}[/tex]
c)
[tex]-2(x-4)(x+5)\geq 0\ |:(-2)\\(x-4)(x+5)\leq 0\\x\in < -5,4 >[/tex]
d)
[tex]-1 < -(1-x)^2\\(1-x)^2-1 < 0\\(1-x-1)(1-x+1) < 0\\-x(-x+2) < 0\\-x*(-1)(x-2) < 0\\x(x-2) < 0\\x\in(0,2)[/tex]
