Quadratic equations and inequalities

Solve the following quadratic equation. \[ -x^{2} + 12x - 20 = 0 \]

Identify an equation which does not have at least one solution in the interval \((0;\infty )\).

Identify an equation which does not have the set \(K = \{ - 3;6\}\) as the set of all solutions of this equation.

Which of the given equations have at least one root the same? \[ \begin{aligned} x^{2} + 8x + 15 & = 0 &\text{(1)} \\x^{2} - 8x + 15 & = 0 &\text{(2)} \\x^{2} +\phantom{ 8}x - 12 & = 0 &\text{(3)} \\x^{2} - 2x -\phantom{ 1}8 & = 0 &\text{(4)} \\\end{aligned}\]