20q^3-26q^2-210=0

asked by guest
on Nov 16, 2024 at 8:46 am



You asked:

Solve the equation \(20 \cdot {q}^{3} - 26 \cdot {q}^{2} - 210 = 0\) for the variable \(q\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}q &= \frac{13}{30} + \sqrt[3]{\frac{143947}{27000} + \frac{\sqrt{159845}}{75}} + \frac{169}{900 \sqrt[3]{\frac{143947}{27000} + \frac{\sqrt{159845}}{75}}} \approx 2.7196212\\q &= - \frac{\sqrt[3]{\frac{\sqrt{159845}}{75} + \frac{143947}{27000}}}{2} - \frac{169}{1800 \sqrt[3]{\frac{\sqrt{159845}}{75} + \frac{143947}{27000}}} + \frac{13}{30} + i \left(- \frac{169 \sqrt{3}}{1800 \sqrt[3]{\frac{\sqrt{159845}}{75} + \frac{143947}{27000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{159845}}{75} + \frac{143947}{27000}}}{2}\right) \approx -0.70981059 + 1.832212 i\\q &= - \frac{\sqrt[3]{\frac{\sqrt{159845}}{75} + \frac{143947}{27000}}}{2} - \frac{169}{1800 \sqrt[3]{\frac{\sqrt{159845}}{75} + \frac{143947}{27000}}} + \frac{13}{30} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{159845}}{75} + \frac{143947}{27000}}}{2} + \frac{169 \sqrt{3}}{1800 \sqrt[3]{\frac{\sqrt{159845}}{75} + \frac{143947}{27000}}}\right) \approx -0.70981059 -1.832212 i\end{aligned}\]

\(i\) is the imaginary unit, defined as \(i^2 = -1\).

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