The solution is:
[tex]x = \frac{-3+\sqrt{51}i}{6}\ \ \ \ AND\ \ \ \ x = \frac{-3-\sqrt{51}i}{6}[/tex]
Step-by-step explanation:
Given equation is:
[tex]3x^2+3x+5 = 0[/tex]
We will use the quadratic formula for solving the given equation
The quadratic formula is:
[tex]x = \frac{-b+\sqrt{b^2-4ac}}{2a}\ \ \ ,\ \ \ x = \frac{-b-\sqrt{b^2-4ac}}{2a}[/tex]
Here,
a = 3
b = 3
c = 5
[tex]x = \frac{-3+\sqrt{(3)^2-4(3)(5)}}{2(3)}\ \ \ ,\ \ \ x = \frac{-3-\sqrt{(3)^2-4(3)(5)}}{2(3)}\\x = \frac{-3+\sqrt{9-60}}{6}\ \ \ ,\ \ \ x = \frac{-3-\sqrt{9-60}}{6}\\x = \frac{-3+\sqrt{-51}}{6} \ \ \ , \ \ \ \ x = \frac{-3-\sqrt{-51}}{6}[/tex]
As we know
[tex]i = \sqrt{-1}[/tex]
So,
[tex]x=\frac{-3+\sqrt{51*-1}}{6} \ \ \ , \ \ \ \ x = \frac{-3-\sqrt{51*-1}}{6}\\x=\frac{-3+(\sqrt{51}*\sqrt{-1})}{6} \ \ \ , \ \ \ \ x = \frac{-3-(\sqrt{51}*\sqrt{-1})}{6}\\x = \frac{-3+\sqrt{51}i}{6}\ \ \ \ AND\ \ \ \ x = \frac{-3-\sqrt{51}i}{6}[/tex]
Hence,
The solution is:
[tex]x = \frac{-3+\sqrt{51}i}{6}\ \ \ \ AND\ \ \ \ x = \frac{-3-\sqrt{51}i}{6}[/tex]
Keywords: Quadratic equation, quadratic formula
Learn more about quadratic equation at:
- brainly.com/question/10941043
- brainly.com/question/10978510
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