Answer:
[tex]x=\frac{-\sqrt{13} -5}{6}[/tex] or [tex]x=\frac{\sqrt{13} -5}{6}[/tex]
Step-by-step explanation:
The given quadratic equation is
[tex]3x^2+5x+1=0[/tex]
When we compare to the general quadratic equation,
[tex]ax^2+bx+c=0[/tex], then we have
[tex]a=3,b=5,c=1[/tex]
The quadratic formula is given by,
[tex]x=\frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
We substitute the given values into the formula to obtain,
[tex]x=\frac{-5\pm \sqrt{5^2-4(3)(1)} }{2(3)}[/tex]
This simplifies to,
[tex]x=\frac{-5\pm \sqrt{25-12} }{2(3)}[/tex]
This further simplifies to,
[tex]x=\frac{-5\pm \sqrt{13} }{6}[/tex]
We split the plus or minus sign to obtain,
[tex]x=\frac{-\sqrt{13} -5}{6}[/tex] or [tex]x=\frac{\sqrt{13} -5}{6}[/tex]
