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$\sqrt{x^2-5x+6}+\sqrt{x-x^2+20}=\sqrt{9x^2-3x-60}$
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$$\sqrt{x^2-5x+6}+\sqrt{x-x^2+20}=\sqrt{9x^2-3x-60}$$

$$\Longleftrightarrow x^2-5x+6+x-x^2+20+2.\sqrt{(x^2-5x+6).(x-x^2+20)}=9x^2-3x-60$$

$$\Longleftrightarrow 2.\sqrt{(x-3)(x-2)(5-x)(x+4)}=9x^2+x-86$$

$$\left\{\begin{matrix}a=\sqrt{(x-3)(x+4)}=\sqrt{x^2+x-12} & \\ b=\sqrt{(5-x)(x-2)}=\sqrt{-x^2+7x-10} & \end{matrix}\right. a;b \ge 0$$

$$\rightarrow 2ab=8a^2-b^2$$

$$\Longleftrightarrow (2a-b)(4a+b)=0$$

$$\Longleftrightarrow ...$$
 
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