Explanation:
The expression is given below as
[tex]4x^2-4x+10=0[/tex]To find the solution, we will use the quadratic formula below
[tex]\begin{gathered} x_{1.2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ where, \\ a=4,b=-4,c=10 \end{gathered}[/tex]By substituign the values, we will have
[tex]\begin{gathered} x_{1.2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x_{1.2}=\frac{-(-4)\pm\sqrt{(-4)^2-4(4\times10)}}{2\times4} \\ x_{1.2}=\frac{4\pm\sqrt{16-160}}{8} \\ x_{1.2}=\frac{4\pm\sqrt{-144}}{8} \\ recall\sqrt{-144}=12i \\ x_{1.2}=\frac{4\pm12i}{8} \\ x_1=\frac{4}{8}+\frac{12i}{8},x_2=\frac{4}{8}-\frac{12i}{8} \\ x_1=\frac{1}{2}+\frac{3}{2}i,x_2=\frac{1}{2}-\frac{3}{2}i \end{gathered}[/tex]Hence,
The final answer is
[tex]x_=\frac{1}{2}+\frac{3}{2}\imaginaryI\text{ }or\text{ }x=\frac{1}{2}-\frac{3}{2}\imaginaryI[/tex]