Question

question 9 of 10, step 1 of 1 solve the following quadratic equation using the quadratic formula. separate multiple answers with a comma if necessary. \\(-3y^2 + 2y + 3 = 0\\) answer

Explanation:

Step1: Identify coefficients

For equation $-3y^2 + 2y + 3 = 0$, we have $a=-3$, $b=2$, $c=3$.

Step2: Recall quadratic formula

The quadratic formula is $y=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$.

Step3: Calculate discriminant

$\Delta = b^2-4ac = 2^2 - 4(-3)(3) = 4 + 36 = 40$

Step4: Substitute into formula

$$\begin{align*} y&=\frac{-2\pm\sqrt{40}}{2(-3)}\\ &=\frac{-2\pm2\sqrt{10}}{-6}\\ &=\frac{1\mp\sqrt{10}}{3} \end{align*}$$

Answer:

$y=\frac{1+\sqrt{10}}{3}, \frac{1-\sqrt{10}}{3}$