Add 3 to both sides so that the equation becomes 2x^2 + 6x + 2 = 0.
To find the solutions to this equation, we can apply the quadratic formula. This quadratic formula solves equations of the form ax^2 + bx + c = 0
x = [ -b ± √(b^2 - 4ac) ] / (2a)
x = [-6 ± √(6^2 - 4(2)(2)) ] / ( 2(2) )
x = [-6 ± √(36 - (16) ) ] / ( 4 )
x = [-6 ± √(20) ] / ( 4)
x = [-6 ± 2*sqrt(5) ] / ( 4 )
x = -3/2 ± sqrt(5)/2
The answers are -3/2 + sqrt(5)/2 and -3/2 - sqrt(5)/2.