How do you solve $4x^2=12x-11$ ?

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Answer 1 · 2015-09-22T16:43:13

The solutions are
$color(blue)( (12+sqrt(-32))/8$

$color(blue)( (12-sqrt(-32))/8$

$4x^2=12x−11$

$4x^2 - 12x + 11 = 0$

The equation is of the form $color(blue)(ax^2+bx+c=0$ where:
$a=4, b=-12, c=11$

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

$= (-12)^2-(4* 4 * 11)$

$= 144-176 = -32$

As $Delta<0$ there are no real solutions

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

$x = (-(-12)+-sqrt(-32))/(2*4) = (12+-sqrt(-32))/8$

The solutions are
$color(blue)( (12+sqrt(-32))/8$
$color(blue)( (12-sqrt(-32))/8$

How do you solve 4x^2=12x-114x^2=12x-11?