Solve for u:
4 u^2+4 u+1 = 75
Divide both sides by 4:
u^2+u+1/4 = 75/4
Write the left hand side as a square:
(u+1/2)^2 = 75/4
Take the square root of both sides:
u+1/2 = (5 sqrt(3))/2 or u+1/2 = -(5 sqrt(3))/2
Subtract 1/2 from both sides:
u = (5 sqrt(3))/2-1/2 or u+1/2 = -(5 sqrt(3))/2
Subtract 1/2 from both sides:
Answer: |u = (5 sqrt(3))/2 - 1/2 = -4.8301270.. or u = -1/2 - (5 sqrt(3))/2== 3.8301270
+129840 4u^2+4u+1=75 subtract 75 from both sides
4u^2 + 4u - 74 = 0 divide through by 2
2u^2 + 2u - 37 = 0 since this won't factor, use the quadratic formula
u = [ -2 ± √ [ 2^2 - 4(2)(-37)] / 4 =
[ -2 ± √ [4 + 296 ] / 4 =
[ -2 ± √ [300 ] / 4 =
[-2 ± √ 10√3 ] / 4 =
[ -1 ± 5√3 ] / 2
