# Solve / Reduce runs overnight - should I keep waiting?

I'm pretty new to Mathematica and I'm trying to solve a system of two equations, but both Solve[] and Reduce[] have been running overnight. I managed to get an output for a similar system but mathematica's result was 98,999 pages long and incomprehensible. I would like to ask whether I might be doing something wrong, because I was able to reduce the system to two 4th order polynomials by hand and I know those have an explicit solution so this should be doable.

Here are my queries:

Solve[{b*dp^2 + (d + a + (c - d)*sp)*dp - a == 0 &&
f*sp^2 + (h + e + (g - h)*dp)*sp - e == 0 && a > 0 && b > 0 &&
c > 0 && d > 0 && e > 0 && f > 0 && g > 0  && dp > 0 &&
sp > 0}, {dp, sp}]


and

Reduce[(l^2 - p)*dp^4 + (2*l*m - q)*dp^3 + (2*l*n + m^2 - r)*dp^2 +
2*m*n*dp + n^2 - s == 0 && dp > 0, dp]


They have both been running for ~11 hours now with no result. Anything I can do about this?

• Not really this is a large system with a lot of symbols and probably not optimized, it's definitely not going to run correctly. Even the reduce without dp > 0. You need to reduce somehow, and simply either by hand or with Simplify and try again. – Vahagn Tumanyan Sep 9 '16 at 11:57
• Just stop it. Even without running it is clear that your first system is equivalent to a general 4th order algebraic equation. No simplification is possible. You will get a solution if you remove all these assumptions, but it will be long and not useful. – yarchik Sep 9 '16 at 12:01