Solve 0.5*5*x^2=6

$$0.5 \times 5 \times { x }^{ 2 } =6$$

Solve for x

$$x = \frac{2 \sqrt{15}}{5} \approx 1.549193338$$

$$x = -\frac{2 \sqrt{15}}{5} \approx -1.549193338$$

Steps by Finding Square Root

Multiply 0.5 and 5 to get 2.5.

$$2.5x^{2}=6$$

Divide both sides by 2.5.

$$x^{2}=\frac{6}{2.5}$$

Expand \frac{6}{2.5} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{60}{25}$$

Reduce the fraction \frac{60}{25} to lowest terms by extracting and canceling out 5.

$$x^{2}=\frac{12}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{15}}{5} x=-\frac{2\sqrt{15}}{5}$$

Steps Using the Quadratic Formula

Multiply 0.5 and 5 to get 2.5.

$$2.5x^{2}=6$$

Subtract 6 from both sides.

$$2.5x^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2.5 for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2.5\left(-6\right)}}{2\times 2.5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2.5\left(-6\right)}}{2\times 2.5}$$

Multiply -4 times 2.5.

$$x=\frac{0±\sqrt{-10\left(-6\right)}}{2\times 2.5}$$

Multiply -10 times -6.

$$x=\frac{0±\sqrt{60}}{2\times 2.5}$$

Take the square root of 60.

$$x=\frac{0±2\sqrt{15}}{2\times 2.5}$$

Multiply 2 times 2.5.

$$x=\frac{0±2\sqrt{15}}{5}$$

Now solve the equation x=\frac{0±2\sqrt{15}}{5} when ± is plus.

$$x=\frac{2\sqrt{15}}{5}$$

Now solve the equation x=\frac{0±2\sqrt{15}}{5} when ± is minus.

$$x=-\frac{2\sqrt{15}}{5}$$

The equation is now solved.

$$x=\frac{2\sqrt{15}}{5} x=-\frac{2\sqrt{15}}{5}$$