how do I solve a quadratics equation

Take for example, the equation

13a   +   6a²   =   −6

rearrange the questions into the form         ax²+bx+c=0

6a² + 13a + 6 = 0

method 1: cross-multiplication method

you use the cross multiplication method to find the common factors

3                      2

2                      3

____________________

3×2=6                        2×3=6

(you get 6a²)   (you get 6)

imagine a cross in the middle

3×3+2×2=13 (you reach the middle number 13a)

so you know this set of numbers are correct, so you can come to the answer

(3a+2) (2a+3)=0

JUST TO CHECK THAT YOU HAVE GOT A CORRECT ANSWER

you can check your work by expanding the brackets

like this

(3a+2)(2a+3)

=3a(2a+3)+2(2a+3)

=6a²+9a+4a+6   (simplify)

=6a²+13a+6  (same as the original question, so you know you have factorized it right)

àsolve the problem

3a+2=0 or 2a+3=0

a=    −⅔   or     −3/2

method 2: quadratic formula

if you find the cross-multiplication method too complicated, you can use the quadratic formula

6a² + 13a + 6 = 0

           −b ± √(b² − 4ac)
answers=   _____________________
                     2a

in this case,

a=6

b=13

c=6

(derived from the arranged form of the equation given)

substitute these numbers into the formula

answers

= (−13)+√(13²−4(6)(6))   ÷2(6)        or      = (−13)+√(13²−4(6)(6))   ÷2(6)

=    −⅔                                                        or     −3/2

for both methods, you get the same solutions