It has only "complex" solution:
Solve for x:
4 x^2+8 x+23 = 0
Divide both sides by 4:
x^2+2 x+23/4 = 0
Subtract 23/4 from both sides:
x^2+2 x = -23/4
Add 1 to both sides:
x^2+2 x+1 = -19/4
Write the left hand side as a square:
(x+1)^2 = -19/4
Take the square root of both sides:
x+1 = (i sqrt(19))/2 or x+1 = 1/2 (-i) sqrt(19)
Subtract 1 from both sides:
x = (i sqrt(19))/2-1 or x+1 = 1/2 (-i) sqrt(19)
Subtract 1 from both sides:
Answer: | x = (i sqrt(19))/2-1 or x = 1/2 (-i) sqrt(19)-1
