solving Definition and 4 Threads

Given the following equation: R = ((Q-P) / |Q-P|) ⋅ V where Q, P, and V are 3 dimensional vectors, R is a scalar, "⋅" denotes the dot product, and |Q-P| is the magnitude of Q-P. Assuming Q, V, and R are known and given 3 independent equations with different values for Q, V, and R that...

Would we also use Newton's method, or are there more powerful methods? Are there general methods for solving equations with fractional exponents? The solution to this problem is; https://www.wolframalpha.com/input?i=solve+x%5E%2817%2F6%29+%2B+x%5E%2821%2F25%29+%3D+15

Is there a better way of solving this, My steps, ##5(x+1)^{1.5}-4x-28=0## ##(x+1)^{1.5}=\dfrac{4x+28}{5}## ##(x+1)^3=(\dfrac{4x+28}{5})^2## ##x^3+3x^2+3x+1=\dfrac{16(x+7)^2}{25}## ##25x^3+75x^2+75x+25=16(x^2+14x+49)## ##25x^3+59x^2-149x-759=0## Letting ##f(x)=25x^3+59x^2-149x-759=0## and using...

I need any idea. I haven't made any progress in solving the problem.