Question 1089503
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<pre>
Introduce new variable y = x^3. Then your equation takes the form

5y^2 - 8y = 4.


5y^2 - 8y - 4 = 0,


{{{y[1,2]}}} = {{{(8 +- sqrt(8^2 -4*5*(-4)))/(2*5)}}} = {{{(8 +- sqrt(144))/10}}} = {{{(8 +- 12)/10}}}.


1.  {{{y[1]}}} = {{{(8+12)/10}}} = 2  ====>  x^3 = 2  ====>  x = {{{root(3,2)}}}.


2.  {{{y[2]}}} = {{{(8-12)/10}}} = {{{-0.4}}}  ====>   x^3 = -0.4  ====>  x = {{{-root(3,0.4)}}}.
</pre>

Solved.