- WE WANT TO SOLVE 
THE QUADRATIC EQUATION
4X/SQUARED - 12X + 9 = 0
USING THE QUADRATIC FORMULA 
PROVIDED HERE IN RED
WHERE "A", B, AND C 
ARE THE COEFFICIENTS
OF THE DEGREE TWO TERM, 
THE DEGREE ONE TERM
AND THE CONSTANT.
SO WE NEED TO RECOGNIZE 
THAT "A" IS = 4,
BECAUSE OF THE - SIGN HERE 
B = -12 AND C = +9.
AND NOW FOR THE FIRST STEP
WE'LL PERFORM SUBSTITUTION 
INTO THE QUADRATIC FORMULA
WITHOUT PERFORMING 
ANY CALCULATIONS.
SO WE'LL HAVE X = --12 + OR - 
THE SQUARE ROOT OF -12/SQUARED
MINUS 4 x 4 x 9.
AND WE HAVE THE DENOMINATOR 
OF 2 x 4.
AND NOW WE'LL BEGIN TO SIMPLIFY.
SO WE'LL HAVE X 
= THIS IS GOING TO BE +12
+ OR - THE SQUARE ROOT--
THE NUMBER UNDERNEATH HERE 
IS CALLED THE DISCRIMINANT
AND WE'LL DO THIS IN STEPS.
- 12/SQUARED IS 144
AND THEN WE'LL HAVE - 4 x 4 x 9 
= 144 AS WELL,
ALL OVER 2 x 4
WHICH IS EQUAL TO 8.
NOTICE OUR DISCRIMINANT HERE 
IS GOING TO BE 0.
SO WE'LL HAVE X = 12 + OR - 
THE SQUARED OF 0
WHICH IS ACTUALLY JUST 0 
DIVIDED BY 8.
SO WE HAVE X = 12 + OR - 0 
ALL OVER 8,
WELL ADDING AND SUBTRACTING 0 
ISN'T GOING TO CHANGE ANYTHING.
SO HERE WE ONLY HAVE 
ONE SOLUTION.
WE HAVE X = 12/8 
WHICH DOES SIMPLIFY.
THE GREATEST COMMON FACTOR OF 12 
AND 8 IS 4.
SO WE CAN DIVIDE BOTH BY 4.
SO OUR SOLUTION IS X = 3/2.
AND THIS TELLS US 
SEVERAL THINGS,
BECAUSE IT'S REAL AND RATIONAL
THE DIVISIONAL EQUATION 
WAS FACTORABLE
AND IN FACT IT'S A PERFECT 
SQUARE TRINOMIAL.
IF WE TRIED TO FACTOR THIS
IT'S EQUAL TO THE QUANTITY 
2X - 3/SQUARED
AND BECAUSE WE HAVE TWO FACTORS 
OF 2X - 3
WE SAY THE SOLUTION 
HAS THE MULTIPLICITY OF 2
OR THAT IT'S A DOUBLE 0 
OR A DOUBLE ROOT.
WE'LL TAKE A LOOK AT ANOTHER 
EXAMPLE IN THE NEXT VIDEO.
