Simplify to find theta, my brain is fuzzled from to much work today

smell5
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2(exponential^theta)^2 - 10 = 6(exponential ^theta)
 
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It's a simple quadratic equation a*x^2 + b*x + c = 0 , where x = e^theta.
You can do it, don't give up. ;)
 
Quadratic too.
 
Could it not be set up as 2e^(2x)-6e^x = 10?
 
Just a gentle reminder to homework helpers: we help people do their problem, rather than doing the problem (or all of the thinking) for him.

If he's too fuzzled to work on the problem, then he needs to wait until he can clear his head and start on the problem himself before he can post here.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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