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Algebra
Question

In 1545, a method of solving a cubic equation of the form

$$x ^ { 3 } + m x = n$$

developed by Niccolo Tartaglia, was published in the Ars Magna, a work by Girolamo Cardano. The formula for finding the one real solution of the equation is

$$x \equiv \sqrt[ 3 ] { \frac { n } { 2 } + \sqrt { ( \frac { n } { 2 } ) ^ { 2 } + ( \frac { m } { 3 } ) ^ { 3 } } } - \sqrt[ 3 ] { \frac { - n } { 2 } + \sqrt { ( \frac { n } { 2 } ) ^ { 2 } + ( \frac { m } { 3 } ) ^ { 3 } } }$$

121. $$x ^ { 3 } + 9 x = 26$$