Question

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

Answer 1

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

Answer 2

Answer:

$x=-\frac{2}{3}\\ or\\x=-5$

Step-by-step 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;

$x=\frac{-b\frac{+}{}\sqrt{b^2-4ac} }{2a}$

a=3

b=17

c=10

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

$x=\frac{-17\frac{+}{}\sqrt{289-120} }{6}$

$x=\frac{-17\frac{+}{}\sqrt{169} }{6}$

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

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$x=-\frac{17}{6}+\frac{13}{6}\\x=-\frac{4}{6}\\ x=-\frac{2}{3}$

or

$x=-\frac{17}{6}-\frac{13}{6}\\x=-\frac{30}{6} \\x=-5$