+129840 10 * 6√x ≤ 2 * 6 - √x - 8 first....divide through by 2
5 * 6√x ≤ 1 - 4 next.....multiply both sides by 6√x
5 * 6 2√x ≤ 1 - 4* 6√x add 4* 6√x to both sides....subtract 1 from both sides
5 * 6 2√x + 4* 6√x -1 ≤ 0 let 6√x = u ..... so 6 2√x = u^2....... and we have
5u^2 + 4u - 1 ≤ 0 factor
(5u - 1) (u + 1) ≤ 0 set both factors to 0 and we have that
u = 1/5 and u = -1
If u = -1 then 6√x = -1 which is impossible
If u = 1/5 then 6√x = 1/5
Taking the log of both sides, we have that
log [ 6 √x ] = log (1/5) and we can write
√x log 6 = log (1/5) divide both sides by log 6
√x = log (1/5) / log (6) ≈ -0.8982444 ...but this is impossible because a positive root cannot have a negative evaluation
Thus......there are no [real ] solutions to this problem
Wolframalpha confirms this :
https://www.wolframalpha.com/input/?i=solve+10+%C2%A0*+6%5E%E2%88%9Ax%C2%A0%E2%89%A4+%C2%A0+2+*+6%5E(+-%C2%A0%E2%88%9Ax)+%C2%A0+-+8
