Question

find all complex solutions of $2x^2 - 3x + 6 = 0$. if there is more than one solution, separate them with commas. $x = \square$

Explanation:

Step1: Identify quadratic coefficients

For $2x^2 - 3x + 6 = 0$, $a=2$, $b=-3$, $c=6$

Step2: Use quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Step3: Compute discriminant

$\Delta = b^2-4ac = (-3)^2 - 4(2)(6) = 9 - 48 = -39$

Step4: Substitute into formula

$x=\frac{-(-3)\pm\sqrt{-39}}{2(2)}=\frac{3\pm i\sqrt{39}}{4}$

Answer:

$\frac{3 + i\sqrt{39}}{4}, \frac{3 - i\sqrt{39}}{4}$