The quadratic equation is,
[tex]4x^2-2x+5=0[/tex]
The quadratic equation ax^2 + bx + c = 0 can be solved by quadratic formula as,
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]
The value of a is 4, value of b is -2 and value of c is 5.
Solve the quadratic equation by quadratic formula.
[tex]\begin{gathered} x=\frac{-(-2)\pm\sqrt[]{(-2)^2-4\cdot4\cdot5}}{2\cdot4} \\ =\frac{2\pm\sqrt[]{4-80}}{8} \\ =\frac{2\pm\sqrt[]{-76}}{8} \\ =\frac{2\pm2\sqrt[]{19}i}{8} \\ =\frac{2}{8}\pm\frac{2\sqrt[]{19}}{8}i \\ =\frac{1}{4}+i\frac{\sqrt[]{19}}{4},\frac{1}{4}-i\frac{\sqrt[]{19}}{4} \end{gathered}[/tex]
So answer is,
[tex]x=\frac{1}{4}+i\frac{\sqrt[]{19}}{4},\frac{1}{4}-i\frac{\sqrt[]{19}}{4}[/tex]
