[tex]y=4x^2-2x-5\\\\a=4, \ b=-2, \ c=-5\\\\\Delta=b^2-4ac\rightarrow(-2)^2-4\cdot4\cdot(-5)=4+80=84\\\\\sqrt{\Delta}=\sqrt{84}=\sqrt{4\cdot21}=2\sqrt{21}\\\\x_1=\frac{-b-\sqrt{\Delta}}{2a}\rightarrow\frac{-(-2)-2\sqrt{21}}{2\cdot4}=\frac{2-2\sqrt{21}}{8}=\frac{1-\sqrt{21}}{4}\\\\x_2=\frac{-b+\sqrt{\Delta}}{2a}\rightarrow\frac{-(-2)+2\sqrt{21}}{2\cdot4}=\frac{2+2\sqrt{21}}{8}=\frac{1+\sqrt{21}}{4}[/tex]
[tex]y = 4x^{2}-2x-5\\\\a = 4, \ b = -2, \ c = -5\\\\\Delta = b^{2}-4ac = (-2)^{2}-4\cdot4\cdot(-5) = 4 + 80 = 84\\\\\sqrt{\Delta} = \sqrt{84} = \sqrt{4\cdot21} = 2\sqrt{21}\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{-(-2)-2\sqrt{21}}{2\cdot4} = \frac{2-2\sqrt{1}}{8} = \frac{1-\sqrt{21}}{4}\\\\x_2 = \frac{-b+\sqrt{\Delta}}{4a} = \frac{-(-2)+2\sqrt{21}}{8} = \frac{2+2\sqrt{21}}{8} = \frac{1+\sqrt{21}}{4}[/tex]