18. \( -5 m^{2}+4 m+3=0 \)

Solve the equation \( -5m^{2}+4m+3=0 \). Solve the quadratic equation by following steps: - step0: Solve using the quadratic formula: \(-5m^{2}+4m+3=0\) - step1: Multiply both sides: \(5m^{2}-4m-3=0\) - step2: Solve using the quadratic formula: \(m=\frac{4\pm \sqrt{\left(-4\right)^{2}-4\times 5\left(-3\right)}}{2\times 5}\) - step3: Simplify the expression: \(m=\frac{4\pm \sqrt{\left(-4\right)^{2}-4\times 5\left(-3\right)}}{10}\) - step4: Simplify the expression: \(m=\frac{4\pm \sqrt{76}}{10}\) - step5: Simplify the expression: \(m=\frac{4\pm 2\sqrt{19}}{10}\) - step6: Separate into possible cases: \(\begin{align}&m=\frac{4+2\sqrt{19}}{10}\\&m=\frac{4-2\sqrt{19}}{10}\end{align}\) - step7: Simplify the expression: \(\begin{align}&m=\frac{2+\sqrt{19}}{5}\\&m=\frac{4-2\sqrt{19}}{10}\end{align}\) - step8: Simplify the expression: \(\begin{align}&m=\frac{2+\sqrt{19}}{5}\\&m=\frac{2-\sqrt{19}}{5}\end{align}\) - step9: Rewrite: \(m_{1}=\frac{2-\sqrt{19}}{5},m_{2}=\frac{2+\sqrt{19}}{5}\) Las soluciones de la ecuación \( -5m^{2}+4m+3=0 \) son \( m_{1}=\frac{2-\sqrt{19}}{5} \) y \( m_{2}=\frac{2+\sqrt{19}}{5} \).