Solve 5x^2/8=2/5

$$\frac { 5 x ^ { 2 } } { 8 } = \frac { 2 } { 5 }$$

Solve for x

$$x=\frac{4}{5}=0.8$$

$$x=-\frac{4}{5}=-0.8$$

Steps Using Difference of Squares

Multiply both sides by 8.

$$5x^{2}=\frac{2}{5}\times 8$$

Multiply \frac{2}{5} and 8 to get \frac{16}{5}.

$$5x^{2}=\frac{16}{5}$$

Subtract \frac{16}{5} from both sides.

$$5x^{2}-\frac{16}{5}=0$$

Multiply both sides by 5.

$$25x^{2}-16=0$$

Consider 25x^{2}-16. Rewrite 25x^{2}-16 as \left(5x\right)^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5x-4\right)\left(5x+4\right)=0$$

To find equation solutions, solve 5x-4=0 and 5x+4=0.

$$x=\frac{4}{5} x=-\frac{4}{5}$$

Steps by Finding Square Root

Multiply both sides by 8.

$$5x^{2}=\frac{2}{5}\times 8$$

Multiply \frac{2}{5} and 8 to get \frac{16}{5}.

$$5x^{2}=\frac{16}{5}$$

Divide both sides by 5.

$$x^{2}=\frac{\frac{16}{5}}{5}$$

Express \frac{\frac{16}{5}}{5} as a single fraction.

$$x^{2}=\frac{16}{5\times 5}$$

Multiply 5 and 5 to get 25.

$$x^{2}=\frac{16}{25}$$

Take the square root of both sides of the equation.

$$x=\frac{4}{5} x=-\frac{4}{5}$$

Steps Using the Quadratic Formula

Multiply both sides by 8.

$$5x^{2}=\frac{2}{5}\times 8$$

Multiply \frac{2}{5} and 8 to get \frac{16}{5}.

$$5x^{2}=\frac{16}{5}$$

Subtract \frac{16}{5} from both sides.

$$5x^{2}-\frac{16}{5}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -\frac{16}{5} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-\frac{16}{5}\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-\frac{16}{5}\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-\frac{16}{5}\right)}}{2\times 5}$$

Multiply -20 times -\frac{16}{5}.

$$x=\frac{0±\sqrt{64}}{2\times 5}$$

Take the square root of 64.

$$x=\frac{0±8}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±8}{10}$$

Now solve the equation x=\frac{0±8}{10} when ± is plus. Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$x=\frac{4}{5}$$

Now solve the equation x=\frac{0±8}{10} when ± is minus. Reduce the fraction \frac{-8}{10} to lowest terms by extracting and canceling out 2.

$$x=-\frac{4}{5}$$

The equation is now solved.

$$x=\frac{4}{5} x=-\frac{4}{5}$$