Let p and q are the roots.

Then, according to Vieta's theorem,

p + q =  = 12.

The second condition is 

p - q = 18.


So, you have this system of equations

p + q = 12,
p - q = 18.

Add the equations. You will get

2p = 12 + 18 = 30.

Hence, p = 15.

Then q = 12 - p = 12 - 15 = -3.


Thus the roots are 15 and -3.

Then, according to Vieta's theorem,  = 15*(-3) = -45.

Then c = 2*(-45) = -90.


Answer.  c = -90, and the roots are 15 and -3.

Let zeroes (roots) be 

Then:  =====>  =====>  ------ eq (i)

Also,  ----- Given ------ eq (ii)

 ------ Adding eqs (ii) & (i)





 ------- Substituting 15 for  in eq (i)





Also,  ======> 





 --------- Cross-multiplying

 

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