Question

solve for y.
3y² + 14y + 15 = 0
write each solution as an integer, proper fraction, or improper fraction in simplest form.
if there are multiple solutions, separate them with commas.
y =

Explanation:

Step1: Identify coefficients

For the quadratic equation $3y^{2}+14y + 15=0$, $a = 3$, $b=14$, $c = 15$.

Step2: Calculate the discriminant

The discriminant $\Delta=b^{2}-4ac=(14)^{2}-4\times3\times15=196 - 180=16$.

Step3: Use the quadratic formula

The quadratic formula is $y=\frac{-b\pm\sqrt{\Delta}}{2a}$. Substitute the values: $y=\frac{-14\pm\sqrt{16}}{2\times3}=\frac{-14\pm4}{6}$.

Step4: Find the two solutions

For the plus - sign: $y_1=\frac{-14 + 4}{6}=\frac{-10}{6}=-\frac{5}{3}$.
For the minus - sign: $y_2=\frac{-14-4}{6}=\frac{-18}{6}=- 3$.

Answer:

$-3,-\frac{5}{3}$