Solve the equation for x, where x is a real number (5 points): -3x^2 + 4x - 31 = 23

Do you realize that you have given out 50 points? 

Step One
Start by subtracting 23 from both sides.
-3x^2 + 4x - 31 -23 = 0
-3x^2 + 4x - 54 = 0

This does not give you a real result. We'll solve it anyway

Step two
bring out the quadratic equation and solve that
a = - 3
b = 4
c = -54






x = 0.666 +/- 2 sqrt(158)i/ - 6x = 0.666 -/+ 4.1899ix1 = 0.666 - 4.1899ix2 = 0.666 + 4.1899i