Question 213525
To solve the equation, first factor the polynomial on the left side of the equation.

{{{x^4-7x^3+18x-126=0}}}
{{{(x^4-7x^3)+(18x-126)=0}}} .....  grouping terms
{{{(x^4-7x^3)+(18x-18*7)=0}}}
{{{x^3(x-7)+18(x-7)=0}}}
{{{(x-7)(x^3-18)=0}}}
So {{{x - 7 = 0}}}  or {{{x^3-18=0}}}
From x-7 = 0 we have x = 7
From {{{x^3-18=0}}} we have x=18^(1/3)