t^2=(1/a)*(b^2+(1/c)*(d^2+(1/e)*(f^2)))
Solve for b
You asked:
Solve the equation \[{t}^{2} = \frac{1}{a} \cdot \left({b}^{2} + \frac{1}{c} \cdot \left({d}^{2} + \frac{1}{e} \cdot {f}^{2}\right)\right)\] for the unknown \(b\).
MathBot Answer:
$$\begin{aligned}b &= \frac{\sqrt{\frac{t^{2} a c e - d^{2} e - f^{2}}{c}}}{e^{\frac{1}{2}}}\\b &= - \frac{\sqrt{\frac{t^{2} a c e - d^{2} e - f^{2}}{c}}}{e^{\frac{1}{2}}}\end{aligned}$$