Hello from MrBillDoesMath!
Answer:    -.28 and   -2.72
Discussion:
This is a quadratic equation (where a = 4, b +12, and c = 3 using the standard notation involved in the solution)
 4x^2 + 3= -12x  =>   (given). Add 12x to both sides
4x^2 + 12x + 3 = 0.
From the quadratic formula:
x =   ( -12 +\- sqrt ( 12^2 - 4(4)(3) )    )/ (2 * 4)
x =   ( -12 +\- sqrt (144 -48))/ (2 * 4)      
x =  ( -12 +\- sqrt (96))  / (2 * 4)    
x = ( -12 +\- sqrt(16*6) ) / (2 * 4)
The "+" solution,    x = -12/8  + ( 4 /8)sqrt(6) =  -3/2 + 1/2 (sqrt(6)) =  -.28
The "-" solution     x = -12/8  -  ( 4 /8)sqrt(6)  =  -3/2 - 1/2 (sqrt(6)) = -2.72
Regards,
MrB