Need help on exponential equation

http://oi45.tinypic.com/hvxa2r.jpg

I did the quadratic formula and it gave me 12, which my online homework assignment says is incorrect. Please help! Thank you!

almost!
you should have gotten 2 answers: 3 and 12
3+12 = 15

the EQ is x^2 -15x +36 =0

quad formula or factor
(x-3)(3-12)=0

so 3 and 12 are solutions for x

I took this last year!
3^(x^2) = 9^(7.5x-18)
What you need to do is have equal bases. So let's stick with having 9 as a base. So put 9 as your base and put it to the power half times x^2 (orginal exponent), in order to still make it equal to 9). Or you can use 3 as a base and just use 3^2 times the original base (7.5x-18) for the one on the right.
9^.5(x^2) = 9^(7.5x-18)
Now solve.
9^(.5x^2) = 9^(7.5x-18)
0.5x^2 = 7.5x-18
0.5x^2 -7.5x +18
0.5(x^2-15x+36)
You get (x-3)(x-12)

So your answers are 3 and 12.

3^(x^2) = 9^( (15/2) x - 18)
3^(x^2) = 3^2( (15/2) x - 18)
3^(x^2) = 3^( (15) x - 36)

x^2 = 15x - 36
x^2 - 15x + 36 = 0
(x - 12)(x - 3) = 0

x = 12 is one solution
x = 3 is the other solution.

Did it give you the opportunity to put in two answers.
a and b are the two solutions
3 + 12 = 15. That is what you should feed in.

look slike you are going to need to use logs
[which I suck at]
but
9=3^2
so
3^(x^2)=9^(15x/2-18)
becomes
3^(x^2)=3^2(15x/2-18)

hey
looks like algebra works
x^2=2(15x/2-18)
x^2=15x-36
x^2-15x+36

(x-12)(x-3)

x=3,12

too bad your assignment did not say you were half right. :)

3^x^2 = 96(15x/2 - 18)

Take logs:
x^2 Log 3 = (15x/2 -18) Log 9

x^2 / (15x/2 -18) = Log 9 / Log 3 = 2

x^2 = 2( 15x/2 - 18)
x^2 - 15x + 36 = 0
(x - 12)(x - 3) = 0
x = 3 or 12

So, (a+b) = 15

3^(x^2) = 9^(15x/2 - 18)

3^(x^2) = (3^2)^(15x/2 - 18)

3^(x^2) = 3^(15x - 36)

x^2 = 15x - 36

x^2 - 15x + 36 = 0

(x - 12)(x-3) = 0

x = 12,3 = a,b

a+b = 12+3 = 15

3^(x^2) = 9^[(15/2)x - 18]

3^(x^2) = 3^[2(15/2)x - 18]

3^(x^2) = 3^(15x - 36)

x^2 = 15x - 36

x^2 - 15x + 36 = 0

(x - 3)(x - 12) = 0

x = {3, 12}

x² = 15x - 36
x² - 15x + 36 = 0
(x - 12) (x - 3) = 0
x = 12 , x = 3