a) [latex]2(x+1)^2=5(4-x)\ 2(x^2+2x+1)=20-5x\ 2x^2+4x+2-20+5x=0\ 2x^2+9x-18=0\ Delta = b^{2}-4ac\ Delta = 81-4*2*(-18)=81+144=225\ sqrt{Delta}=15\ x_{1}=frac {-b-sqrt {Delta}}{2a}\ x_{2}=frac {-b+sqrt {Delta}}{2a}\ x_{1}=frac {-9-15}{4}=-6\ x_{2}=frac {-9+15}{4}=1,5[/latex] b) [latex]x^2+sqrt{2x}-4=0\ Delta = b^{2}-4ac\ Delta = 2-4*1*(-4)=18\ sqrt{Delta }=3sqrt{2}\ x_{1}=frac {-b-sqrt {Delta}}{2a}=frac {-sqrt{2}-3sqrt{2}}{2}=frac {-4sqrt{2}}{2}=-2sqrt{2}\ x_{2}=frac {-b+sqrt {Delta}}{2a}=frac {-sqrt{2}+3sqrt{2}}{2}=frac {2sqrt{2}}{2}=sqrt{2} [/latex] c) [latex]sqrt{3x^2}- 9x + 6sqrt{3}=0\ Delta = b^{2}-4ac\ Delta = 81-4*sqrt{3}*6sqrt{3}=81-72=9\ sqrt{ Delta}=3\ x_{1}=frac {-b-sqrt {Delta}}{2a}=frac {9-3}{2sqrt{3}}=frac {6}{2sqrt{3}}=frac {3}{sqrt{3}}*frac {sqrt{3}}{sqrt{3}}=frac {3sqrt{3}}{3}=sqrt{3}\ x_{2}=frac {-b+sqrt {Delta}}{2a}=frac {9+3}{2sqrt{3}}=frac {12}{2sqrt{3}}=frac {6}{sqrt{3}}*frac {sqrt{3}}{sqrt{3}}=frac {6sqrt{3}}{3}=2sqrt{3}[/latex]
