If $x$ is real, prove that $2x^2-6x+9$ is always positive______.

Find for what real values of $x$, the expression :

$x^2+8x+15=0$

Prove that $8\mathrm{x}-15-{\mathrm{x}}^2>0$ for limited values of $\mathrm{x}$ and also find the limits:

Direction: In the following question, two equations numbered I and II are given. You have to solve both the equation.

$\text{ I. }\sqrt{25{\mathrm{x}}^2}-125=0$

$\text{ II. }\sqrt{361}+95=0$

Direction: In the following question, two equations numbered I and II are given. You have to solve both the equation.

$\text{ I. }\frac{5}{7}-\frac{5}{21}=\frac{\sqrt{\mathrm{x}}}{42}$

$\text{ II. }\frac{\sqrt{\mathrm{y}}}{4}+\frac{\sqrt{\mathrm{y}}}{16}=\frac{250}{\sqrt{\mathrm{y}}}$