Answer:
[tex]\sf x=1+i\sqrt{\dfrac{2}{3}} \ \quad and \quad \:x=1-i\sqrt{\dfrac{2}{3}}[/tex]
Explanation:
Given Expression:
Use the Quadratic Formula:
[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ \ ax^2 + bx + c = 0[/tex]
insert coefficients
[tex]\Longrightarrow \sf x = \dfrac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:3\cdot \:5}}{2\cdot \:3}[/tex]
[tex]\Longrightarrow \sf x = \dfrac{\left6\right\pm \sqrt{-24} }{6}[/tex]
[tex]\Longrightarrow \sf x = \dfrac{\left6\right\pm 2\sqrt{6}i}{6}[/tex]
[tex]\Longrightarrow \sf x =1 \pm i\dfrac{\sqrt{6} }{3}[/tex]
[tex]\Longrightarrow \sf x=1+i\sqrt{\dfrac{2}{3}}, \quad 1-i\sqrt{\dfrac{2}{3}}[/tex]
