How do you solve $10v² = 13v + 3$ ?

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Answer 1 · 2016-03-26T14:46:14

The solutions are:
$v = 3/2$

$v = -1 /5$

$10v^2 = 13v +3$

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

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:

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

$= (-13)^2-(4* 10 * (-3))$

$= 169 + 120 = 289$

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

$v = (-(-13)+-sqrt(289))/(2*10) = (13+-17)/20$

$v = (13+17)/20 = 30 / 20 = 3/2$

$v = (13-17)/20 = -4/ 20 = -1 /5$

How do you solve 10v² = 13v + 310v² = 13v + 3?