# How do you solve 10v² = 13v + 3?

Mar 26, 2016

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

$v = - \frac{1}{5}$

#### Explanation:

$10 {v}^{2} = 13 v + 3$

$10 {v}^{2} - 13 v - 3 = 0$

The equation is of the form color(blue)(av^2+bv+c=0 where:
$a = 10 , b = - 13 , c = - 3$

The Discriminant is given by:

color(green)(Delta=b^2-4*a*c

$= {\left(- 13\right)}^{2} - \left(4 \cdot 10 \cdot \left(- 3\right)\right)$

$= 169 + 120 = 289$

The solutions are found using the formula
color(green)(v=(-b+-sqrtDelta)/(2*a)

$v = \frac{- \left(- 13\right) \pm \sqrt{289}}{2 \cdot 10} = \frac{13 \pm 17}{20}$

$v = \frac{13 + 17}{20} = \frac{30}{20} = \frac{3}{2}$

$v = \frac{13 - 17}{20} = - \frac{4}{20} = - \frac{1}{5}$