Question

solve the following quadratic equation using the quadratic formula. separate multiple answers with a comma if necessary.
6y² + 2y - 1 = 0

Explanation:

Step1: Identify coefficients

For $6y^2 + 2y - 1 = 0$, $a=6$, $b=2$, $c=-1$

Step2: Recall quadratic formula

$$y=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

Step3: Compute discriminant

$\Delta = b^2-4ac = 2^2 - 4(6)(-1) = 4 + 24 = 28$

Step4: Substitute into formula

$$y=\frac{-2\pm\sqrt{28}}{2(6)}=\frac{-2\pm2\sqrt{7}}{12}$$

Step5: Simplify the fraction

$$y=\frac{-1\pm\sqrt{7}}{6}$$

Answer:

$\frac{-1+\sqrt{7}}{6}, \frac{-1-\sqrt{7}}{6}$