Solve:

$x^2-4x-12=0;$ when $x\in I$

Solve:

$2x^2-9x+10=0;$ when $x\in Q$.

Solve:

${\left(a+b\right)}^2{x}^2-(a+b)x-6=0; a+b\ne 0.$

Solve:

$\frac{1}{p}+\frac{1}{q}+\frac{1}{x}=\frac{1}{x+p+q}$

Solve:

$x(x+1)+(x+2)(x+3)=42$

Solve:

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

For each equation, given below, find the value of $\text{'}\mathrm{m}\text{'}$so that the equation has equal roots. Also, find the solution of each equation :

$(m-3)x^2-4x+1=0$

For each equation, given below, find the value of $\text{'}\mathrm{m}\text{'}$so that the equation has equal roots. Also, find the solution of each equation :

$3x^2+12x+(m+7)=0$

For each equation, given below, find the value of $\text{'}\mathrm{m}\text{'}$so that the equation has equal roots. Also, find the solution of each equation :

$x^2-(m+2)x+(m+5)=0$