Solve 6-1.2x^2=0

$$6-1.2 { x }^{ 2 } =0$$

Solve for x

$$x=\sqrt{5}\approx 2.236067977$$

$$x=-\sqrt{5}\approx -2.236067977$$

Steps by Finding Square Root

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$-1.2x^{2}=-6$$

Divide both sides by -1.2.

$$x^{2}=\frac{-6}{-1.2}$$

Expand \frac{-6}{-1.2} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{-60}{-12}$$

Divide -60 by -12 to get 5.

$$x^{2}=5$$

Take the square root of both sides of the equation.

$$x=\sqrt{5} x=-\sqrt{5}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-1.2x^{2}+6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1.2 for a, 0 for b, and 6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1.2\right)\times 6}}{2\left(-1.2\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1.2\right)\times 6}}{2\left(-1.2\right)}$$

Multiply -4 times -1.2.

$$x=\frac{0±\sqrt{4.8\times 6}}{2\left(-1.2\right)}$$

Multiply 4.8 times 6.

$$x=\frac{0±\sqrt{28.8}}{2\left(-1.2\right)}$$

Take the square root of 28.8.

$$x=\frac{0±\frac{12\sqrt{5}}{5}}{2\left(-1.2\right)}$$

Multiply 2 times -1.2.

$$x=\frac{0±\frac{12\sqrt{5}}{5}}{-2.4}$$

Now solve the equation x=\frac{0±\frac{12\sqrt{5}}{5}}{-2.4} when ± is plus.

$$x=-\sqrt{5}$$

Now solve the equation x=\frac{0±\frac{12\sqrt{5}}{5}}{-2.4} when ± is minus.

$$x=\sqrt{5}$$

The equation is now solved.

$$x=-\sqrt{5} x=\sqrt{5}$$