Question

solve for y.
\\(3y^2 + 6 = -11y\\)
if there is more than one solution, separate them with
if there is no solution, click on
o solution\.

Explanation:

Step1: Rearrange to standard quadratic form

$3y^2 + 11y + 6 = 0$

Step2: Apply quadratic formula

For $ay^2+by+c=0$, $y=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Here $a=3$, $b=11$, $c=6$.
$$y=\frac{-11\pm\sqrt{11^2-4\times3\times6}}{2\times3}$$

Step3: Calculate discriminant

$\sqrt{121-72}=\sqrt{49}=7$

Step4: Compute two solutions

$y_1=\frac{-11+7}{6}=\frac{-4}{6}=-\frac{2}{3}$
$y_2=\frac{-11-7}{6}=\frac{-18}{6}=-3$

Answer:

$y = -3$ and $y = -\frac{2}{3}$