Solve 5/6b^4-900b^2+735000=0

$$\frac { 5 } { 6 } b ^ { 4 } - 900 b ^ { 2 } + 735000 = 0$$

Solve for b

$$b=2\sqrt[4]{55125}e^{\frac{-\arctan(\frac{2\sqrt{41}}{9})i+2\pi i}{2}}\approx -27.195114916+14.127075963i$$

$$b=2\sqrt[4]{55125}e^{-\frac{\arctan(\frac{2\sqrt{41}}{9})i}{2}}\approx 27.195114916-14.127075963i$$

$$b=2\sqrt[4]{55125}e^{\frac{\arctan(\frac{2\sqrt{41}}{9})i+2\pi i}{2}}\approx -27.195114916-14.127075963i$$

$$b=2\sqrt[4]{55125}e^{\frac{\arctan(\frac{2\sqrt{41}}{9})i}{2}}\approx 27.195114916+14.127075963i$$

Steps Using the Quadratic Formula

Substitute t for b^{2}.

$$\frac{5}{6}t^{2}-900t+735000=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute \frac{5}{6} for a, -900 for b, and 735000 for c in the quadratic formula.

$$t=\frac{-\left(-900\right)±\sqrt{\left(-900\right)^{2}-4\times \frac{5}{6}\times 735000}}{\frac{5}{6}\times 2}$$

Do the calculations.

$$t=\frac{900±\sqrt{-1640000}}{\frac{5}{3}}$$

Solve the equation t=\frac{900±\sqrt{-1640000}}{\frac{5}{3}} when ± is plus and when ± is minus.

$$t=540+120\sqrt{41}i t=-120\sqrt{41}i+540$$

Since b=t^{2}, the solutions are obtained by evaluating b=±\sqrt{t} for each t.

$$b=2\sqrt[4]{55125}e^{\frac{\arctan(\frac{2\sqrt{41}}{9})i+2\pi i}{2}} b=2\sqrt[4]{55125}e^{\frac{\arctan(\frac{2\sqrt{41}}{9})i}{2}} b=2\sqrt[4]{55125}e^{-\frac{\arctan(\frac{2\sqrt{41}}{9})i}{2}} b=2\sqrt[4]{55125}e^{\frac{-\arctan(\frac{2\sqrt{41}}{9})i+2\pi i}{2}}$$