Answer:
[tex]x=-\frac{2}{3}\\ or\\x=-5[/tex]
Step-by-step explanation:
[tex]3x^2+17x+4=-6[/tex]
add 6 on both sides.
[tex]3x^2+17x+4+6=-6+6[/tex]
[tex]3x^2+17x+10=0[/tex]
Solve using the quadratic formula;
[tex]x=\frac{-b\frac{+}{}\sqrt{b^2-4ac} }{2a}[/tex]
a=3
b=17
c=10
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[tex]x=\frac{-(17)\frac{+}{}\sqrt{(17)^2-4(3)(10)} }{2(3)}[/tex]
[tex]x=\frac{-17\frac{+}{}\sqrt{289-120} }{6}[/tex]
[tex]x=\frac{-17\frac{+}{}\sqrt{169} }{6}[/tex]
[tex]x=\frac{-17\frac{+}{}13 }{6}[/tex]
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[tex]x=-\frac{17}{6}+\frac{13}{6}\\x=-\frac{4}{6}\\ x=-\frac{2}{3}[/tex]
or
[tex]x=-\frac{17}{6}-\frac{13}{6}\\x=-\frac{30}{6} \\x=-5[/tex]
