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you can not solve this equation
To solve an equation with three unknowns, x, y and z, you require 3 independent equations.
The equation 7 x + 14 y + 10 z = 98001 has infinite solutions. For any x and y we can have a z which satisfies this equation. For example, if we choose x=1 and y=1 then z=9798 satisfies. To have a specific solution there must be three equations for three unknowns (x,y,z), which can be solved simultaneously.
If x = y and y = z then x = z
To find what z-score represents the 80th percentile, simply solve for 0.8 = F(z), where F(x) is the standard normal cumulative distribution function. Solving gives us: z = 0.842