2x^2-5x+312=0

Solution for 2x^2-5x+312=0 equation:

Simplifying
2x2 + -5x + 312 = 0

Reorder the terms:
312 + -5x + 2x2 = 0

Solving
312 + -5x + 2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
156 + -2.5x + x2 = 0

Move the constant term to the right:

Add '-156' to each side of the equation.
156 + -2.5x + -156 + x2 = 0 + -156

Reorder the terms:
156 + -156 + -2.5x + x2 = 0 + -156

Combine like terms: 156 + -156 = 0
0 + -2.5x + x2 = 0 + -156
-2.5x + x2 = 0 + -156

Combine like terms: 0 + -156 = -156
-2.5x + x2 = -156

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = -156 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = -156 + 1.5625

Combine like terms: -156 + 1.5625 = -154.4375
1.5625 + -2.5x + x2 = -154.4375

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = -154.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.