The quadratic fomula:
[tex]ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\If\ \Delta<0,\ then\ \boxed{NO\ SOLUTION}\\\\If\ \Delta=0,\ then\ \boxed{ONE\ SOLUTION:\ x=\dfrac{-b}{2a}}\\\\If\ \Delta>0,\ then\ \boxed{TWO\ SOLUTIONS:\ x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}}-----------------------------------------------[/tex]
We have the equation:
[tex]2x^2-7x-21=0\\\\a=2,\ b=-7,\ c=-21\\\\\Delta=(-7)^2-4(2)(-21)=49+168=217 > 0\\\\x_1=\dfrac{-(-7)-\sqrt{217}}{2(2)}=\dfrac{7-\sqrt{217}}{4}\approx-1.93\\\\x_2=\dfrac{-(-7)+\sqrt{217}}{(2)(2)}=\dfrac{7+\sqrt{217}}{4}\approx5.43\\\\Answer:\ \boxed{\boxed{2.\ -1.93\ and\ 5.43}}[/tex]
