b) $$ 5 x^{2}+13 x+6=\varnothing $$ $$ 5 x^{2}+13 x+6=\varnothing $$

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Para resolver la ecuación cuadrática $$ 5 x^{2} + 13 x + 6 = 0 $$, utilizaremos la fórmula general para las ecuaciones cuadráticas, que es:

$$
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
$$

donde $$ a = 5 $$, $$ b = 13 $$ y $$ c = 6 $$.

Primero, calcularemos el discriminante $$ b^2 - 4ac $$:

$$
b^2 - 4ac = 13^2 - 4 \cdot 5 \cdot 6
$$

Ahora, procederé a calcular el discriminante y luego resolveré la ecuación.
Calculate the value by following steps:
- step0: Calculate:
  $$13^{2}-4\times 5\times 6$$
- step1: Multiply the terms:
  $$13^{2}-120$$
- step2: Evaluate the power:
  $$169-120$$
- step3: Subtract the numbers:
  $$49$$
Calculate or simplify the expression $$ -13 + \sqrt(49) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$-13+\sqrt{49}$$
- step1: Simplify the root:
  $$-13+7$$
- step2: Add the numbers:
  $$-6$$
Calculate or simplify the expression $$ -13 - \sqrt(49) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$-13-\sqrt{49}$$
- step1: Simplify the root:
  $$-13-7$$
- step2: Subtract the numbers:
  $$-20$$
Calculate or simplify the expression $$ \frac{-6}{10} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{-6}{10}$$
- step1: Reduce the fraction:
  $$\frac{-3}{5}$$
- step2: Rewrite the fraction:
  $$-\frac{3}{5}$$
Calculate or simplify the expression $$ \frac{-20}{10} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{-20}{10}$$
- step1: Reduce the numbers:
  $$\frac{-2}{1}$$
- step2: Calculate:
  $$-2$$
Ahora que hemos calculado el discriminante y obtenido los valores de $$ x $$, continuemos con los pasos:

1. El discriminante es $$ 49 $$, lo que significa que hay dos soluciones reales.
2. Calculamos las soluciones usando la fórmula cuadrática:

- Para $$ x_1 $$:
   $$
   x_1 = \frac{-13 + \sqrt{49}}{2 \cdot 5} = \frac{-13 + 7}{10} = \frac{-6}{10} = -\frac{3}{5} \quad \text{o} \quad -0.6
   $$

- Para $$ x_2 $$:
   $$
   x_2 = \frac{-13 - \sqrt{49}}{2 \cdot 5} = \frac{-13 - 7}{10} = \frac{-20}{10} = -2
   $$

Por lo tanto, las soluciones de la ecuación $$ 5 x^{2} + 13 x + 6 = 0 $$ son:

$$
x_1 = -\frac{3}{5} \quad \text{y} \quad x_2 = -2
$$
Las soluciones de la ecuación $$ 5x^{2} + 13x + 6 = 0 $$ son $$ x = -\frac{3}{5} $$ y $$ x = -2 $$.

b)

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