Answer:
[tex]x=\dfrac{-5+\sqrt{13}}{6}, \quad x=\dfrac{-5-\sqrt{13}}{6}[/tex]
Step-by-step explanation:
The quadratic formula is a mathematical expression used to find the solutions of a quadratic equation of the form ax² + bx + c = 0.
[tex]\boxed{\begin{array}{l}\underline{\sf Quadratic\;Formula}\\\\x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\textsf{when} \;ax^2+bx+c=0 \\\end{array}}[/tex]
For the equation 3x² + 5x + 1 = 0, the coefficients a, b and c are:
[tex]a = 3\\\\b = 5\\\\c = 1[/tex]
Substitute these values into the quadratic formula and solve for x:
[tex]x=\dfrac{-5 \pm \sqrt{5^2-4(3)(1)}}{2(3)}\\\\\\\\x=\dfrac{-5 \pm \sqrt{25-12}}{6}\\\\\\\\x=\dfrac{-5 \pm \sqrt{13}}{6}[/tex]
Therefore, the solutions to the equation 3x² + 5x + 1 = 0 are:
[tex]\large\boxed{\boxed{x=\dfrac{-5+\sqrt{13}}{6}, \quad x=\dfrac{-5-\sqrt{13}}{6}}}[/tex]
