Answer:
The x-interecepts are 5.6 and -1.4, approximately.
Step-by-step explanation:
The given equation is
[tex]5x^{2} -21x=39[/tex]
Where [tex]a=5[/tex], [tex]b=-21[/tex] and [tex]c=39[/tex], let's use the quadratic formula
[tex]x_{1,2}=\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a} =\frac{-(-21) (+-)\sqrt{(-21)^{2} -4(5)(-39)} }{2(5)}\\ x_{1,2}=\frac{21(+-)\sqrt{441+780} }{10}=\frac{21(+-35)}{10}\\x_{1}=\frac{21+35}{10}=\frac{56}{10} \approx 5.6\\ x_{2}=\frac{21-35}{10}=\frac{-14}{10} \approx -1.4[/tex]
Therefore, the x-interecepts are 5.6 and -1.4, approximately.
