Answer:
[tex]x=-\frac{17}{8}+\frac{\sqrt{97} }{8}[/tex] or [tex]x=-\frac{17}{8}-\frac{\sqrt{97} }{8}[/tex]
Step-by-step explanation:
[tex]x^2+17x+12=-3x^2[/tex]
Add [tex]3x^2[/tex] on both sides.
[tex]x^2+17x+12+3x^2=-3x^2+3x^2[/tex]
[tex]x^2+17x+12+3x^2=0[/tex]
Combine like terms;
[tex]4x^2+17x+12=0[/tex]
Use the quadratic formula;
a=4
b=17
c=12
[tex]x=\frac{-b\frac{+}{}\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=\frac{-(17)\frac{+}{}\sqrt{(17)^2-4(4)(12)} }{2(4)}[/tex]
[tex]x=\frac{-17\frac{+}{}\sqrt{289-192} }{8}[/tex]
[tex]x=\frac{-17\frac{+}{}\sqrt{97} }{8}[/tex]
[tex]x=-\frac{17}{8}+\frac{\sqrt{97} }{8}[/tex] or [tex]x=-\frac{17}{8}-\frac{\sqrt{97} }{8}[/tex]
