Solve 6x^4+7x^2-3=0

$$6 x ^ { 4 } + 7 x ^ { 2 } - 3 = 0$$

Solve for x (complex solution)

$$x=\frac{\sqrt{3}}{3}\approx 0.577350269$$

$$x=-\frac{\sqrt{3}}{3}\approx -0.577350269$$

$$x=-\frac{\sqrt{6}i}{2}\approx -0-1.224744871i$$

$$x=\frac{\sqrt{6}i}{2}\approx 1.224744871i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$6t^{2}+7t-3=0$$

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, 7 for b, and -3 for c in the quadratic formula.

$$t=\frac{-7±\sqrt{7^{2}-4\times 6\left(-3\right)}}{2\times 6}$$

Do the calculations.

$$t=\frac{-7±11}{12}$$

Solve the equation t=\frac{-7±11}{12} when ± is plus and when ± is minus.

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

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

$$x=-\frac{\sqrt{3}}{3} x=\frac{\sqrt{3}}{3} x=-\frac{\sqrt{6}i}{2} x=\frac{\sqrt{6}i}{2}$$

Solve for x

$$x=-\frac{\sqrt{3}}{3}\approx -0.577350269$$

$$x=\frac{\sqrt{3}}{3}\approx 0.577350269$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$6t^{2}+7t-3=0$$

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, 7 for b, and -3 for c in the quadratic formula.

$$t=\frac{-7±\sqrt{7^{2}-4\times 6\left(-3\right)}}{2\times 6}$$

Do the calculations.

$$t=\frac{-7±11}{12}$$

Solve the equation t=\frac{-7±11}{12} when ± is plus and when ± is minus.

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

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

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