Solve for x:
x^2 + x + 5 = 90
Subtract 5 from both sides:
x^2 + x = 85
Add 1/4 to both sides:
x^2 + x + 1/4 = 341/4
Write the left hand side as a square:
(x + 1/2)^2 = 341/4
Take the square root of both sides:
x + 1/2 = sqrt(341)/2 or x + 1/2 = -sqrt(341)/2
Subtract 1/2 from both sides:
x = sqrt(341)/2 - 1/2 or x + 1/2 = -sqrt(341)/2
Subtract 1/2 from both sides:
Answer: |x = sqrt(341)/2 - 1/2 or x = -1/2 - sqrt(341)/2
