Answer:
[tex]x_1=\frac{3(2+i\sqrt{6})}{10}[/tex]
[tex]x_2=\frac{3(2-i\sqrt{6})}{10}[/tex]
Step-by-step explanation:
Use the Quadratic formula:
[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
You can identify that, in this case:
[tex]a=-10\\b=12\\c=-9[/tex]
Now you need to substitute these values into the formula:
[tex]x=\frac{-12\±\sqrt{12^2-4(-10)(-9)}}{2(-10)}[/tex]
[tex]x=\frac{-12\±\sqrt{-216}}{-20}[/tex]
Remember that:
[tex]i=\sqrt{-1}[/tex]
Therefore,rewriting and simplifying, you get:
[tex]x=\frac{-12\±6i\sqrt{6}}{-20}[/tex]
[tex]x=\frac{-6(2\±i\sqrt{6})}{-2(10)}[/tex]
[tex]x=\frac{3(2\±i\sqrt{6})}{10}[/tex]
Then, you get the following roots:
[tex]x_1=\frac{3(2+i\sqrt{6})}{10}[/tex]
[tex]x_2=\frac{3(2-i\sqrt{6})}{10}[/tex]
