Solve -6x^2+12-3=0

$$- 6 x ^ { 2 } + 12 - 3 = 0$$

Solve for x

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

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

Steps by Finding Square Root

Subtract 3 from 12 to get 9.

$$-6x^{2}+9=0$$

Subtract 9 from both sides. Anything subtracted from zero gives its negation.

$$-6x^{2}=-9$$

Divide both sides by -6.

$$x^{2}=\frac{-9}{-6}$$

Reduce the fraction \frac{-9}{-6} to lowest terms by extracting and canceling out -3.

$$x^{2}=\frac{3}{2}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Subtract 3 from 12 to get 9.

$$-6x^{2}+9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -6 for a, 0 for b, and 9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-6\right)\times 9}}{2\left(-6\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-6\right)\times 9}}{2\left(-6\right)}$$

Multiply -4 times -6.

$$x=\frac{0±\sqrt{24\times 9}}{2\left(-6\right)}$$

Multiply 24 times 9.

$$x=\frac{0±\sqrt{216}}{2\left(-6\right)}$$

Take the square root of 216.

$$x=\frac{0±6\sqrt{6}}{2\left(-6\right)}$$

Multiply 2 times -6.

$$x=\frac{0±6\sqrt{6}}{-12}$$

Now solve the equation x=\frac{0±6\sqrt{6}}{-12} when ± is plus.

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

Now solve the equation x=\frac{0±6\sqrt{6}}{-12} when ± is minus.

$$x=\frac{\sqrt{6}}{2}$$

The equation is now solved.

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