Solve equation for $x$ by factorisation

$\frac{1}{x-3}+\frac{2}{x-2}=\frac{8}{x}, x\ne 0, 2, 3$

Solve equation for $x$ by factorisation

$\frac{x-2}{x-3}+\frac{x-4}{x-5}=3\frac{1}{3}, x\ne 3,5$

Solve equation for $x$ by factorisation

$\frac{3}{x+1}+\frac{4}{x-1}=\frac{29}{4x-1}, x\ne -1, 1, \frac{1}{4}$

Solve equation for $x$ by factorisation

$\frac{x+1}{x-1}+\frac{x-2}{x+2}=4-\frac{2x+3}{x-2}, x\ne -1, -2, 2$

Solve for $x$ : $\frac{1}{a+b+x}=\frac{1}{a}+\frac{1}{b}+\frac{1}{x}, a\ne 0, b\ne 0, c\ne 0$

Use the substitution $y=3x+1$ to solve  for $x:$$5{\left(3x+1\right)}^2+6\left(3x+1\right)-8=0$

Solve for $x$ : $\frac{x}{x+1}+\frac{x+1}{x}=2\frac{1}{12}, x\ne 0, -1$

Solve for $x$ : $\sqrt{2x+9}+x=13$

Find the roots of the following quadratic equations, if they exist , using the quadratic formula:

$3x^2-5x+2=0$