[tex]\large\displaystyle\text{$ \mathsf{2x^2-x-3=0}$}[/tex]
[tex]\large\displaystyle\text{$ \mathsf{ \begin{cases}\sf a=2\\\sf b=-1\\\sf c=-3\end{cases} }$}[/tex]
[tex]\large\displaystyle\text{$ \mathsf{ \Delta=b^2-4\cdot a\cdot c }$}[/tex]
[tex]\large\displaystyle\text{$ \mathsf{ \Delta=(-1)^2-4\cdot 2\cdot (-3) }$}[/tex]
[tex]\large\displaystyle\text{$ \mathsf{ \Delta=1+24}$}[/tex]
[tex]\large\displaystyle\text{$ \mathsf{\Delta=25 }$}[/tex]
[tex]\large\displaystyle\text{$ \mathsf{ x=\dfrac{-b\pm\sqrt{\Delta}}{2\cdot a}}$}[/tex]
[tex]\large\displaystyle\text{$ \mathsf{ x=\dfrac{-(-1)\pm\sqrt{25}}{2\cdot2}}$}[/tex]
[tex]\large\displaystyle\text{$ \mathsf{x=\dfrac{1\pm5}{4} \begin{cases}\sf x_1=\dfrac{1+5}{4}=\dfrac{6^{\div2}}{4^{\div2}}=\dfrac{3}{2}\\\\\sf x_2=\dfrac{1-5}{4}=\dfrac{-4}{4}=-1\end{cases}}$}[/tex]
