Explanation

(a)
$\left( \frac{9}{10} \right)^{x} = - 3 + x - x^{2}$
$\Rightarrow \ \left( \frac{9}{10} \right)^{x} = - \left\{ \left( \ x - \frac{1}{2} \right)^{2} + \frac{11}{4} \right\}$
$\Rightarrow$ LHS is always positive while RHS is always negative. Hence, the given equation has no solution.