We can solve a quadratic equation of the form:
[tex]ax^2+bx+c=0[/tex]The quadratic formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Given the equation:
[tex]\begin{gathered} 7x^2+5x-3=0 \\ a=7,b=5,c=-3 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} x=\frac{-5\pm\sqrt{5^2-4\times7\times-3}}{2\times7} \\ =\frac{-5\pm\sqrt{25-(-84)}}{14} \\ =\frac{-5\pm\sqrt{25+84}}{14} \\ =\frac{-5\pm\sqrt{109}}{14} \\ \text{Therefore:} \\ x=\frac{-5+\sqrt{109}}{14}\lor x=\frac{-5-\sqrt{109}}{14} \\ x=0.3886\lor x=-1.1029 \end{gathered}[/tex]
