Solve 6=0.5*9.8*x^2

$$6=0.5 \times 9.8 \times { x }^{ 2 }$$

Solve for x

$$x = \frac{2 \sqrt{15}}{7} \approx 1.10656667$$

$$x = -\frac{2 \sqrt{15}}{7} \approx -1.10656667$$

Steps by Finding Square Root

Multiply 0.5 and 9.8 to get 4.9.

$$6=4.9x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$4.9x^{2}=6$$

Divide both sides by 4.9.

$$x^{2}=\frac{6}{4.9}$$

Expand \frac{6}{4.9} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{60}{49}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{15}}{7} x=-\frac{2\sqrt{15}}{7}$$

Steps Using the Quadratic Formula

Multiply 0.5 and 9.8 to get 4.9.

$$6=4.9x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$4.9x^{2}=6$$

Subtract 6 from both sides.

$$4.9x^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4.9 for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4.9\left(-6\right)}}{2\times 4.9}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4.9\left(-6\right)}}{2\times 4.9}$$

Multiply -4 times 4.9.

$$x=\frac{0±\sqrt{-19.6\left(-6\right)}}{2\times 4.9}$$

Multiply -19.6 times -6.

$$x=\frac{0±\sqrt{117.6}}{2\times 4.9}$$

Take the square root of 117.6.

$$x=\frac{0±\frac{14\sqrt{15}}{5}}{2\times 4.9}$$

Multiply 2 times 4.9.

$$x=\frac{0±\frac{14\sqrt{15}}{5}}{9.8}$$

Now solve the equation x=\frac{0±\frac{14\sqrt{15}}{5}}{9.8} when ± is plus.

$$x=\frac{2\sqrt{15}}{7}$$

Now solve the equation x=\frac{0±\frac{14\sqrt{15}}{5}}{9.8} when ± is minus.

$$x=-\frac{2\sqrt{15}}{7}$$

The equation is now solved.

$$x=\frac{2\sqrt{15}}{7} x=-\frac{2\sqrt{15}}{7}$$