The equation $5{\mathrm{x}}^2-17\mathrm{x}+14=0$ is expressed as ${(\mathrm{x}-\frac{\mathrm{a}}{\mathrm{b}})}^2=\frac{9}{100}$. Find the values of a and b respectively.

Given equation: $5{\mathrm{x}}^2-17\mathrm{x}+14=0$

${\mathrm{x}}^2-\frac{17}{5}\mathrm{x}+\frac{14}{5}=0$

${\mathrm{x}}^2-2\times \frac{17}{10}\times \mathrm{x}+{\left(\frac{17}{10}\right)}^2-{\left(\frac{17}{10}\right)}^2+\frac{14}{5}=0$

${\left(\mathrm{x}-\frac{17}{10}\right)}^2-\frac{9}{100}=0$

Comparing with ${(\mathrm{x}-\frac{\mathrm{a}}{\mathrm{b}})}^2=\frac{9}{100}$, we get:

a = 17, b = 10