Answer:
3, -1/7
Step-by-step explanation:
Use the quadratic formula to solve this problem. First make all terms equal to 0, so subtract 3 from both sides of the equation.
7x^2 - 20x - 3 = 0
Substitute the a, b, and c values into the quadratic formula: [tex]\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]. In this equation:
[tex]\frac{-(-20)\pm\sqrt{(-20)^2-4(7)(-3)} }{2(7)}[/tex]
Simplify this expression until you get to where you have to split the expression off into a positive and negative case.
[tex]\frac{20\pm\sqrt{400-4(-21)} }{14}\rightarrow \frac{20\pm\sqrt{400+84} }{14}\rightarrow \frac{20\pm\sqrt{484} }{14}[/tex]
Now split this into + and -:
[tex]\frac{20\pm\sqrt{484} }{14} ~~becomes~~\frac{20+\sqrt{484} }{14} ~~or~~\frac{20-\sqrt{484} }{14}[/tex]
Solve the positive case first.
[tex]\frac{20+\sqrt{484} }{14} \rightarrow \frac{20+22}{14} \rightarrow\frac{42}{14} =\boxed{3}[/tex]
Solve the negative case next.
[tex]\frac{20-\sqrt{484} }{14} \rightarrow\frac{20-22}{14} \rightarrow\frac{-2}{14} = \boxed{-\frac{1}{7} }[/tex]
These are the two solutions to the quadratic equation.
