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