Solve 2y^2-17y=y^4

$$2 y ^ { 2 } - 17 y = y ^ { 4 }$$

Solve for y

$$y = -\frac{18 ^ {\frac{2}{3}} {(\sqrt[3]{\sqrt{23313} + 153} + \sqrt[3]{153 - \sqrt{23313}})}}{18} \approx -2.829764492$$

$$y=0$$

Steps Using the Quadratic Formula

Subtract y^{4} from both sides.

$$2y^{2}-17y-y^{4}=0$$

Substitute t for y^{2}.

$$-t^{2}+2t-17=0$$

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 -1 for a, 2 for b, and -17 for c in the quadratic formula.

$$t=\frac{-2±\sqrt{2^{2}-4\left(-1\right)\left(-17\right)}}{-2}$$

Do the calculations.

$$t=\frac{-2±\sqrt{-64}}{-2}$$

Since the square root of a negative number is not defined in the real field, there are no solutions.

$$t\in \emptyset$$

Since t=y^{2}, the original equation does not have any solutions.

$$y\in \emptyset$$