solving x^4 - 13x^3 + 31x^2 + 126 = 0 is not easy.
Wolfram is a powerful website that gives us the following:
http://www.wolframalpha.com/input/?i=solve+x%5E4+-+13x%5E3+%2B+31x%5E2+%2B+126%3D0
Notice we have 2 reals, and 2 complex roots.
Since we are given exact real roots of 7 ± √7, suggests that Wolfram used a formula
There is indeed such a formula but it is extremely complicated. Google "solving quartic equations"
If you know Calculus, you should try Netwon's Method
X^4-13X^3+31X^2+126 find the roots
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