make the expression equal to 0
6x² + 13x + 5 = 0
since its in the for ax² + bx + c multiply 'c' by 'a' = 30
now you must find factors of 30 that multiply to give 5 but add to give 13 but since such an equation does't exist as whole numbers then you have to resort to using the formula which states that x =[tex] \frac{-b + or - \sqrt{b^{2} - 4ac } }{2a} [/tex]
so now you just plug in your values a = 6; b= 13 and c= 5
x = [tex] \frac{-13 + or - \sqrt{13^{2} - 4(6)(5) } }{2(6)} [/tex]
= [tex] \frac{-13 + or - \sqrt{169 - 120 } }{12} [/tex]
∴ either x = [tex]\frac{-13 + \sqrt{49 } }{12}[/tex] OR x = [tex]\frac{(-13) - \sqrt{49 } }{12}[/tex]
⇒ x = - [tex] \frac{1}{2} [/tex] OR x = [tex] - \frac{5}{3} [/tex]
∴ 6x² + 13x + 5 = (x + [tex] \frac{1}{2} [/tex]) (x + [tex] \frac{5}{3} [/tex])
