Solve 6x^4-45x^2+81=0

$$6 x ^ { 4 } - 45 x ^ { 2 } + 81 = 0$$

Solve for x

$$x = -\frac{3 \sqrt{2}}{2} \approx -2.121320344$$

$$x = \frac{3 \sqrt{2}}{2} \approx 2.121320344$$

$$x=\sqrt{3}\approx 1.732050808$$

$$x=-\sqrt{3}\approx -1.732050808$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$6t^{2}-45t+81=0$$

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, -45 for b, and 81 for c in the quadratic formula.

$$t=\frac{-\left(-45\right)±\sqrt{\left(-45\right)^{2}-4\times 6\times 81}}{2\times 6}$$

Do the calculations.

$$t=\frac{45±9}{12}$$

Solve the equation t=\frac{45±9}{12} when ± is plus and when ± is minus.

$$t=\frac{9}{2} t=3$$

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

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