[tex]2x^2+3x-4=0[/tex]
resolver con la formula para ecuaciones de segundo grado
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\\\ \mathrm{a=2,\:b=3,\:c=-4}[/tex]
[tex]x_{1,\:2}=\frac{-3\pm \sqrt{3^2-4\cdot \:2\left(-4\right)}}{2\cdot \:2}[/tex]
[tex]x_{1,\:2}=\frac{-3\pm \sqrt{3^2+4\cdot \:2\left(4\right)}}{2\cdot \:2}[/tex]
[tex]x_{1,\:2}=\frac{-3\pm \sqrt{9+4\cdot \:2\left(4\right)}}{2\cdot \:2}[/tex]
[tex]x_{1,\:2}=\frac{-3\pm \sqrt{9+32}}{2\cdot \:2}[/tex]
[tex]x_{1,\:2}=\frac{-3\pm \sqrt{41}}{2\cdot \:2}[/tex]
separar las soluciones
[tex]x_1=\frac{-3+\sqrt{41}}{2\cdot \:2},\:x_2=\frac{-3-\sqrt{41}}{2\cdot \:2}[/tex]
resolvemos
[tex]x_1=\frac{-3+\sqrt{41}}{2\cdot \:2}[/tex]
[tex]x_1=\frac{-3+\sqrt{41}}{4} \longrightarrow \mathrm{primera \:\: soluci\'on}[/tex]
[tex]x_2=\frac{-3-\sqrt{41}}{2\cdot \:2}[/tex]
[tex]x_2=\frac{-3-\sqrt{41}}{4} \longrightarrow \mathrm{segunda \: \: soluci\'on}[/tex]
