How do you solve 3p^2 + 17p= -10?

Mar 18, 2016

Answer:

The solutions are:
$p = - \frac{2}{3}$

$p = - 5$

Explanation:

$3 {p}^{2} + 17 p = - 10$

$3 {p}^{2} + 17 p + 10 = 0$

The equation is of the form color(blue)(ap^2+bp+c=0 where:

$a = 3 , b = 17 , c = 10$

The Discriminant is given by:

$\Delta = {b}^{2} - 4 \cdot a \cdot c$

$= {\left(17\right)}^{2} - \left(4 \cdot 3 \cdot 10\right)$

$= 289 - 120 = 169$

The solutions are found using the formula
$p = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

$p = \frac{- 17 \pm \sqrt{169}}{2 \cdot 3} = \frac{\left(- 17 \pm 13\right)}{6}$

$p = \frac{- 17 + 13}{6} = - \frac{\cancel{4}}{\cancel{6}} = - \frac{2}{3}$

$p = \frac{- 17 - 13}{6} = - \frac{30}{6} = - 5$