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 =\(\frac{-b + or - \sqrt{b^{2} - 4ac } }{2a}\)
so now you just plug in your values a = 6; b= 13 and c= 5
x = \(\frac{-13 + or - \sqrt{13^{2} - 4(6)(5) } }{2(6)}\)
= \(\frac{-13 + or - \sqrt{169 - 120 } }{12}\)
∴ either x = \(\frac{-13 + \sqrt{49 } }{12}\) OR x = \(\frac{(-13) - \sqrt{49 } }{12}\)
⇒ x = - \(\frac{1}{2}\) OR x = \(- \frac{5}{3}\)
∴ 6x² + 13x + 5 = (x + \(\frac{1}{2}\)) (x + \(\frac{5}{3}\))
