[latex]a)\ \ 3x(x+3)= (x+3)^{2} \ \3x^2+9x=x^2+6x+9\ \3x^2+9x-x^2-6x-9 =0 \ \ 2x^2+3x -9 =0 \ \[/latex]
[latex]Delta = b^{2}-4ac = 3^{2}-4*2* (-9)=9+72=81 \ \sqrt{Delta }=sqrt{81}= 9 \ \x_{1}=frac{-b-sqrt{Delta }}{2a} =frac{-3- 9}{2*2}=frac{-12}{4}=-3 \ \ x_{2}=frac{-b+sqrt{Delta }}{2a} =frac{-3+ 9}{2*2}=frac{6}{4}= frac{3}{2}[/latex]
[latex]b) \ 2x^{2} + 7x geq 4 \ \ 2x^{2} + 7x -4 geq 0 \ \ Delta = b^{2}-4ac = 7^{2}-4*2* (-4)=49+32=81[/latex]
[latex]sqrt{Delta }=sqrt{81}= 9 \ \x_{1}=frac{-b-sqrt{Delta }}{2a} =frac{-7- 9}{2*2}=frac{-16}{4}=-4 \ \ x_{2}=frac{-b+sqrt{Delta }}{2a} =frac{-7+ 9}{2*2}=frac{2}{4}= frac{1}{2} \ \a>0 ramiona paraboli skierowane do gory : \ \xin (-infty ,-4> cup
[latex]a)\\3x(x+3) = (x+3)^{2}\\3 x^{2} +9x = x^{2} +6x+9 = 0\\3 x^{2} - x^{2} +9x-6x-9 = 0\\2 x^{2} +3x-9 = 0\\Delta = 9+72 = 81, sqrt{Delta} = 9\\x_1 = frac{-3-9}{4} = frac{-12}{4} = -3\\x_2 = frac{-3+9}{4} = frac{3}{2} = 1,5\\x= -3 V x = 1,5[/latex] [latex]b)\\2 x^{2} + 7x geq 4\\2 x^{2} +7x - 4 geq 0\\Delta = 49+32 = = 81, sqrt{Delta} = 9\\M.Z.:\\x = frac{-7-9}{4} = -4\\x = frac{-7+9}{4} = 0,5[/latex] a = 2 > 0, ramiona paraboli skierowane w górę x ∈ (-∞; -4 > U < 0,5; +∞)
