Answer:
x = -2/3, -1
Step-by-step explanation:
Solve the equation for x by finding a, b, and c of the quadratic then apply the quadratic formula.
For this case we have a quadratic equation of the form [tex]ax ^ 2 + bx + c = 0[/tex], where:
[tex]a = 3\\b = 5\\c = 2[/tex]
The solution of the equation is determined by the quadratic formula, which is given by:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
Substituting the values in the formula we have:
[tex]x = \frac {-5 \pm \sqrt {5 ^ 2-4 (3) (2)}} {2 (3)}\\x = \frac {-5 \pm \sqrt {(25-24)}} {6}\\x = \frac {-5 \pm \sqrt {1}} {6}\\x = \frac {-5 \pm1} {6}[/tex]
So:
[tex]x_ {1} = \frac {-5 + 1} {6} = \frac {-4} {6} = \frac {-2} {3}\\x_ {2} = \frac {-5-1} {6} = \frac {-6} {6} = - 1[/tex]
Answer:
The roots are:
[tex]x_ {1} = \frac {-2} {3}\\x_ {2} = - 1[/tex]
