Solving Quadratic Equations: The Quadratic
Formula, a la Shmoop.
Since the Dark Ages, the alchemists of Eureka,
Incorporated have been trying as hard as they
can to turn lead into gold.
They've experimented with every formula known
to man: the Empirical formula, the Hardy-Weinberg
formula, Formula 409.
Now that they have a new reality show documenting
their efforts, they will try...
...The Quadratic Formula.
First, they have to uncover this ancient formula,
which hasn't been seen by man in thousands
of years....
Wait, what's that?
It's taught in pretty much every high school
math class?
Well, more people today know Ke$ha 
than Euclid, so let's pretend, okay?
This ancient formula reads: x equals negative
b plus-or-minus the square root of b-squared
minus four-a-c over two-a.
In order to work their magic, the alchemists
have to solve for x in this equation:
Three-x-squared equals two-x plus five...
...or face elimination in front of a live
studio audience tomorrow.
First, they need to change the equation into
this form:
a-x squared plus b-x plus c equals zero.
Looks like they're going to subtract two-x
and five from both sides, leaving us with...
...three-x-squared minus two-x minus five
equals zero.
Now it's time to apply the formula.
X equals two plus-or-minus the square root
of negative two squared, minus four times
three times negative five, all this over two
times three.
This simplifies to two plus or minus the square-root
of four plus sixty, over six.
Furthermore, this simplifies to two plus or
minus the square-root of sixty-four over six.
The square-root of sixty-four is eight, and
since our equation is plus or minus...
We have two equations now,
x equals two plus eight over six
and x equals two minus eight over six.
Two plus eight equals ten, so x equals ten
over six, which reduces to five over three.
As for the other one, two minus eight equals
negative six.
Negative six over six reduces to negative
one.
X equals negative one.
And... that's about it.
They didn't turn lead into gold, but they
turned one math problem into two solutions.
That's something, right?
Still, it's better than that time they tried
baby formula.
They ended up with more babies than they knew
what to do with.
