[tex]\displaystyle \\
4x^{2} +3x-1=0 \\ \\
x_{12}= \frac{-b \pm \sqrt{b^2-4ac} }{2a} = \\ \\
=\frac{-3 \pm \sqrt{3^2-4\cdot 4 \cdot (-1)} }{2\cdot 4} = \\ \\
=\frac{-3 \pm \sqrt{9+16} }{8} = \frac{-3 \pm \sqrt{25} }{8} =\boxed{\frac{-3 \pm 5}{8} }\\ \\
x_1 =\frac{-3 + 5}{8} } = \frac{2}{8} } = \boxed{\frac{1}{4} } \\ \\
x_2 =\frac{-3 - 5}{8} } = \frac{-8}{8} } = \boxed{-1 }
[/tex]
