Solve 5*2x^2=9

$$5 \times 2 x ^ { 2 } = 9$$

Solve for x

$$x=\frac{3\sqrt{10}}{10}\approx 0.948683298$$

$$x=-\frac{3\sqrt{10}}{10}\approx -0.948683298$$

Steps by Finding Square Root

Multiply 5 and 2 to get 10.

$$10x^{2}=9$$

Divide both sides by 10.

$$x^{2}=\frac{9}{10}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{10}}{10} x=-\frac{3\sqrt{10}}{10}$$

Steps Using the Quadratic Formula

Multiply 5 and 2 to get 10.

$$10x^{2}=9$$

Subtract 9 from both sides.

$$10x^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 10\left(-9\right)}}{2\times 10}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 10\left(-9\right)}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{0±\sqrt{-40\left(-9\right)}}{2\times 10}$$

Multiply -40 times -9.

$$x=\frac{0±\sqrt{360}}{2\times 10}$$

Take the square root of 360.

$$x=\frac{0±6\sqrt{10}}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{0±6\sqrt{10}}{20}$$

Now solve the equation x=\frac{0±6\sqrt{10}}{20} when ± is plus.

$$x=\frac{3\sqrt{10}}{10}$$

Now solve the equation x=\frac{0±6\sqrt{10}}{20} when ± is minus.

$$x=-\frac{3\sqrt{10}}{10}$$

The equation is now solved.

$$x=\frac{3\sqrt{10}}{10} x=-\frac{3\sqrt{10}}{10}$$