Solve 5m^4+13m^2-6=0

$$5 m ^ { 4 } + 13 m ^ { 2 } - 6 = 0$$

Solve for m

$$m=-\frac{\sqrt{10}}{5}\approx -0.632455532$$

$$m=\frac{\sqrt{10}}{5}\approx 0.632455532$$

Steps Using the Quadratic Formula

Substitute t for m^{2}.

$$5t^{2}+13t-6=0$$

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 5 for a, 13 for b, and -6 for c in the quadratic formula.

$$t=\frac{-13±\sqrt{13^{2}-4\times 5\left(-6\right)}}{2\times 5}$$

Do the calculations.

$$t=\frac{-13±17}{10}$$

Solve the equation t=\frac{-13±17}{10} when ± is plus and when ± is minus.

$$t=\frac{2}{5} t=-3$$

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

$$m=\frac{\sqrt{10}}{5} m=-\frac{\sqrt{10}}{5}$$