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

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

Solve for x

$$x=-\frac{\sqrt{2}}{2}\approx -0.707106781$$

$$x=\frac{\sqrt{2}}{2}\approx 0.707106781$$

$$x = \frac{\sqrt{15}}{3} \approx 1.290994449$$

$$x = -\frac{\sqrt{15}}{3} \approx -1.290994449$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

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

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

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

Do the calculations.

$$t=\frac{-13±7}{-12}$$

Solve the equation t=\frac{-13±7}{-12} when ± is plus and when ± is minus.

$$t=\frac{1}{2} t=\frac{5}{3}$$

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

$$x=\frac{\sqrt{2}}{2} x=-\frac{\sqrt{2}}{2} x=\frac{\sqrt{15}}{3} x=-\frac{\sqrt{15}}{3}$$