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How do you solve $3x^2+8=12x$ by using the Quadratic Formula?

1 Answer

Jul 21, 2015

$x = 2 +- 4/sqrt(3)$
$color(white)("XXXX")$ $color(white)("XXXX")$ (solved using the Quadratic Formula)

Explanation:

Using the standard quadratic form:
$color(white)("XXXX")$ $ax^2+bx+c=0$
the quadratic formula for the solutions is
$color(white)("XXXX")$ $x = (-b+-sqrt(b^2-4ac))/(2a)$

It will be necessary, first to convert the given equation:
$color(white)("XXXX")$ $3x^2+8=12x$
into the standard form (by subtracting $(12x)$ from both sides):
$color(white)("XXXX")$ $3x^2-12x+8 = 0$

Therefore, using:
$color(white)("XXXX")$ $a= 3$ $color(white)("XXXX")$ $b=-12$ $color(white)("XXXX")$ $c=8$

The quadratic formula gives
$color(white)("XXXX")$ $x = (12 +-sqrt((-12)^2 - 4(3)(8)))/(2(3))$

$color(white)("XXXX")$ $x = (12 +-sqrt(144 -96))/6$

$color(white)("XXXX")$ $x = 2 +- 4/sqrt(3)$

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