The quadratic formula is:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]
For a quadratic equation in standard form:
[tex]ax^2+bx+c=0[/tex]
In this case, we have:
[tex]\begin{gathered} a=1 \\ b=5 \\ c=-3 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-5\pm\sqrt[]{(5)^2-4(1)(-3)}}{2(1)} \\ x=\frac{-5\pm\sqrt[]{25+12}}{2} \\ x=\frac{-5\pm\sqrt[]{37}}{2} \end{gathered}[/tex]
The given quadratic equation has two solutions:
• First one
[tex]\begin{gathered} x_1=\frac{-5+\sqrt[]{37}}{2} \\ x_1=-\frac{5}{2}+\frac{\sqrt[]{37}}{2} \end{gathered}[/tex]
• Second one
[tex]\begin{gathered} x_2=\frac{-5-\sqrt[]{37}}{2} \\ x_2=-\frac{5}{2}-\frac{\sqrt[]{37}}{2} \end{gathered}[/tex]
Therefore, the solutions of the given quadratic equation are:
[tex]$\boldsymbol{x=-\frac{5}{2}+\frac{\sqrt[]{37}}{2}}$,$\boldsymbol{x=-\frac{5}{2}-\frac{\sqrt[]{37}}{2}}$[/tex]
