INTRODUCTORY EXERCISES

(6)

Find all real solution(s) for the following 
equations by using the quadratic formula. (Note: some equations may not 
have any real solutions.)

     (a) 3a(a-5) = 4a2 + 10a - 20
     (b) 13x2 +17x + 21 = 4x2 + 5x + 17

(a) 3a2 - 15 = 4a2 + 10a - 20
 a2 + 10a - 5 = 0
Remember, the quadratic formula is 

Here, a = 1, b = 10, and c = -5

So,     -10  sqrt{(10)2 - 4(1)(-5)}
    x = ----------------------------
                     2(1)

        -10  sqrt{120}
    x = -----------------
                2

    x = -5  sqrt{30}


(b) 13x2 +17x + 21 = 4x2 + 5x + 17
     9x2 + 12x + 4 = 0
Remember, the quadratic formula is 

Here, a = 9, b = 12, and c = 4 so

        -12  sqrt{144 - 4(9)(4)}
    x = -------------------------
                  2(9)

         -12  sqrt{144-144}
    x = ---------------------
                  18

    x = -2/3