We need to solve the following equation:
[tex]4x^2-5x+6=0[/tex]This is a quadratic equation, for which we can use the Baskhara equation to determine the roots. This equation is shown below:
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]If we replace the values on the equation, we will be able to determine both roots:
[tex]\begin{gathered} x_{1,2}=\frac{-(-5)\pm\sqrt[]{(-5)^2-4\cdot4\cdot6}}{2\cdot4} \\ x_{1,2}=\frac{5\pm\sqrt[]{25-96}}{8} \\ x_{1,2}=\frac{5\pm\sqrt[]{-71}}{8} \\ x_{1,2}=\frac{5\pm i\sqrt[]{71}}{8} \\ x_{1,2}=\frac{5\pm i8.43}{8} \\ x_1=0.625+i1.05 \\ x_2=0.625-i1.05 \end{gathered}[/tex]The solution to this equation is the pair of complex numbers: 0.625+i1.05 and 0.625-i1.05
