Resolver las siguientes ecuaciobes, aplicando la formu general \( \quad \frac{-b \pm \frac{\sqrt{b^{2}-4 a c}}{2 a}}{} \begin{array}{l}\text { a } \\ \text { a) } 16 x^{2}-4 x-13=0\end{array} \)

Solve the equation \( 16x^2-4x-13=0 \). Solve the quadratic equation by following steps: - step0: Solve using the quadratic formula: \(16x^{2}-4x-13=0\) - step1: Solve using the quadratic formula: \(x=\frac{4\pm \sqrt{\left(-4\right)^{2}-4\times 16\left(-13\right)}}{2\times 16}\) - step2: Simplify the expression: \(x=\frac{4\pm \sqrt{\left(-4\right)^{2}-4\times 16\left(-13\right)}}{32}\) - step3: Simplify the expression: \(x=\frac{4\pm \sqrt{848}}{32}\) - step4: Simplify the expression: \(x=\frac{4\pm 4\sqrt{53}}{32}\) - step5: Separate into possible cases: \(\begin{align}&x=\frac{4+4\sqrt{53}}{32}\\&x=\frac{4-4\sqrt{53}}{32}\end{align}\) - step6: Simplify the expression: \(\begin{align}&x=\frac{1+\sqrt{53}}{8}\\&x=\frac{4-4\sqrt{53}}{32}\end{align}\) - step7: Simplify the expression: \(\begin{align}&x=\frac{1+\sqrt{53}}{8}\\&x=\frac{1-\sqrt{53}}{8}\end{align}\) - step8: Rewrite: \(x_{1}=\frac{1-\sqrt{53}}{8},x_{2}=\frac{1+\sqrt{53}}{8}\) Las soluciones de la ecuación \(16x^2-4x-13=0\) son \(x_{1}=\frac{1-\sqrt{53}}{8}\) y \(x_{2}=\frac{1+\sqrt{53}}{8}\).