Solve the following quadratic equation by using the quadratic formula:

$ab{x}^2+\left(b^2-ac\right)x-bc=0, a\ne 0, b\ne 0$

Solve the following quadratic equation by using the quadratic formula:

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

Solve the following quadratic equation by using the quadratic formula:

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

Solve for $x$

$2\left(\frac{2x-1}{x+3}\right)-3\left(\frac{x+3}{2x-1}\right)=5, x\ne -3, \frac{1}{2}$

State whether the following quadratic equation have two distinct real roots. Justify your answer:

$x^2-3x+4=0$