Question 601880
6x+8y=14

xy=-12

x=-12/y

substitute x 
6*(-12/y) +8y=14

multiply the equation by y
-72 +8y^2=14y

8y^2-14y-72=0
/2
4y^2-7y-36=0
4y^2-7y-36=0
 
You have to factorize . convert the trinomial into a a polynomial with 4 terms by splitting the middle term.
compare with equation ax^2 +bx+c
co-efficient of 1st term -  a=4
co-efficient of second term = b= -7
co-eficient of third term = -36
 
The product ac= 4*-36 = -144
factorize -144 .
group the factors into parts, such that the sum of I part & II part = -7
-144= -2*2*2*2*   3*3
 
-16 & 9 are the factors add them you get -7
multiply them you get -144
 
4y^2-16y+9y-36=0 
49(y-4)+9(y-4)=0
(y-4)(4y+9)=0
y = 4 Or -9/4

plug y in xy =-12 to get x= 3 Or x= 16/3