[tex]x^3+8x=30\\
x^3+8x-30=0\\\\
2.2^3+8\cdot2.2-30=10.648+17.6-30=-1.752\\
2.3^3+8\cdot2.3-30=12.167+18.4-30=0.567
[/tex]
For [tex]x=2.2[/tex] the value of [tex]x^3+8x-30[/tex] is negative, and for [tex]x=2.3[/tex] the value is positive which means between [tex]x=2.2[/tex] and [tex]x=2.3[/tex] there is an x for which the value of [tex]x^3+8x-30[/tex] is equal to 0 and therefore there is a solution.
