SOLUTION: I am trying to solve an equation with 2 variables. I am solving for x. x = 6t^2 - 24t + 24

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Question 321207: I am trying to solve an equation with 2 variables. I am solving for x.
x = 6t^2 - 24t + 24

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

It's already solved for x.  If the left side of an equation 
is " x = " and the letter x does not appear on the right side
at all, then the equation is solved for x. 

Did you mean to say you were solving for t and not x, and
just mistyped?

If so, then to solve for t, then we get zero on one side

x+=+6t%5E2+-+24t+%2B+24

Swap sides 

6t%5E2+-+24t+%2B+24=x

Subtract x from both sides:

6t%5E2+-+24t+%2B+24-x=0

Put parentheses around the last two terms on the left
to show that together they can be used to substitute
for c in the quadratic formula.  This step may be
skipped:

6t%5E2+-+24t+%2B+%2824-x%29=0


Then we use the quadratic formula with a=6, b=-24, c=%2824-x%29

t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+



t+=+%2824+%2B-+sqrt%28576-24%2824-x%29+%29%29%2F12+

t+=+%2824+%2B-+sqrt%28576-576%2B24x%29+%29%2F12+ 

t+=+%2824+%2B-+sqrt%2824x%29+%29%2F12+

t+=+%2824+%2B-+sqrt%284%2A6x%29+%29%2F12+

t+=+%2824+%2B-+2sqrt%286x%29+%29%2F12+

Factor 2 out of the top

t+=+%282%2812+%2B-+sqrt%286x%29%29+%29%2F12+

Cancel the 2 in the top into the 12 on the bottom
getting 6 on the bottom:

t+=+%28cross%282%29%2812+%2B-+sqrt%286x%29%29+%29%2F%286%5Ecross%2812%29%29+

t+=+%2812+%2B-+sqrt%286x%29+%29%2F6+

That's really two solutions:

1.  t+=+%2812+%2B+sqrt%286x%29+%29%2F6+

2.  t+=+%2812+-+sqrt%286x%29+%29%2F6+

Edwin