The difference between the solutions of the equation 5x^2−x−k=0 is 1.8. Find the solutions.

Answer 1

Using the quadratic formula:
x = (1 ± √(1 - 4(5)(-k) )/1-
= (1 + √(1+20k))/10 or x = (1 - √(1+20k))/10

then (1 + √(1+20k))/10 - (1 - √(1+20k))/10 = 1.8
(1 + √(1+20k)) - (1 - √(1+20k)) = 18
2√(1+20k) = 18
√(1+20k) = 9
square both sides, easy after that

Answer 2

a = 5
b = -1
c = -k
x1 = [1 +sqrt (1+20k) ] /10
x2 = [1 -sqrt (1+20k) ] /10

x1-x2 = 1.8
1.8*10 = [1 +sqrt (1+20k) ] [1 -sqrt (1+20k) ]
but we know that a^2-b^2 = (a+b)(a-b)
18 = 1 - (1+20k)
17 = -1 -20 k
18 = -20 k
check my arithmetic and continue to get x1 and x2

Answer 3

whoops, made algebra error, go with Reiny solution