Question

use the quadratic formula to solve. express your answer in simplest form.
$6w^2 + w - 15 = 0$
answer attempt 1 out of 2
additional solution no solution
$w = $
submit answer

Explanation:

Step1: Identify quadratic coefficients

For $6w^2 + w - 15 = 0$, $a=6$, $b=1$, $c=-15$

Step2: Recall quadratic formula

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

Step3: Calculate discriminant

$\Delta = b^2-4ac = 1^2 - 4(6)(-15) = 1 + 360 = 361$

Step4: Compute square root of discriminant

$\sqrt{\Delta} = \sqrt{361} = 19$

Step5: Substitute into formula

$$w=\frac{-1\pm19}{2(6)}$$

Step6: Solve for both roots

First root: $w=\frac{-1+19}{12}=\frac{18}{12}=\frac{3}{2}$
Second root: $w=\frac{-1-19}{12}=\frac{-20}{12}=-\frac{5}{3}$

Answer:

$w=\frac{3}{2}$ or $w=-\frac{5}{3}$