How do you solve $11x^2-x-3=0$ using the quadratic formula?

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Answer 1 · 2015-08-10T07:35:46

The solutions for the equation are:
$color(blue)( x =(1+sqrt(133))/22$
$color(blue)( x =(1-sqrt(133))/22$

$11x^2−x−3 =0$

The equation is of the form $color(blue)(ax^2+bx+c=0$ where:
$a=11, b=-1, c=-3$

The Discriminant is given by:
$Delta=b^2-4*a*c$

$= (-1)^2-(4*11*(-3))$

$=133$

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

$x = (-(-1)+-sqrt(133))/(2*11) = (1+-sqrt(133))/22$

The solutions are:
$color(blue)( x =(1+sqrt(133))/22$
$color(blue)( x =(1-sqrt(133))/22$

How do you solve 11x^2-x-3=011x^2-x-3=0 using the quadratic formula?