Question

Solve for x in the equation 3x^2 + 17x + 4 = -6

Answer 1

`x=-(2)/(3)\\ or\\x=-5`

Explanation:

`3x^2+17x+4=-6`

add 6 on both sides.

`3x^2+17x+4+6=-6+6`

`3x^2+17x+10=0`

Solve using the quadratic formula;

`x=\frac{-b\frac{+}{}√(b^2-4ac) }{2a}`

a=3

b=17

c=10

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`x=\frac{-(17)\frac{+}{}√((17)^2-4(3)(10)) }{2(3)}`

`x=\frac{-17\frac{+}{}√(289-120) }{6}`

`x=\frac{-17\frac{+}{}√(169) }{6}`

`x=\frac{-17\frac{+}{}13 }{6}`

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`x=-(17)/(6)+(13)/(6)\\x=-(4)/(6)\\ x=-(2)/(3)`

or

`x=-(17)/(6)-(13)/(6)\\x=-(30)/(6) \\x=-5`

Answer 2

subtract -6 from both sides
3x^2 + 17x + 4 - (-6) = -6 - (-6)
3x^2 + 17x + 10 = 0

factor left side of equation
(3x+2)(x+5)=0

set factors to 0
x = -2/3 OR x = -5

I would go with -5