Solve 9x^2-15-4=0

$$9 { x }^{ 2 } -15-4=0$$

Solve for x

$$x = \frac{\sqrt{19}}{3} \approx 1.452966315$$

$$x = -\frac{\sqrt{19}}{3} \approx -1.452966315$$

Steps by Finding Square Root

Subtract 4 from -15 to get -19.

$$9x^{2}-19=0$$

Add 19 to both sides. Anything plus zero gives itself.

$$9x^{2}=19$$

Divide both sides by 9.

$$x^{2}=\frac{19}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{19}}{3} x=-\frac{\sqrt{19}}{3}$$

Steps Using the Quadratic Formula

Subtract 4 from -15 to get -19.

$$9x^{2}-19=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and -19 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\left(-19\right)}}{2\times 9}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 9\left(-19\right)}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{0±\sqrt{-36\left(-19\right)}}{2\times 9}$$

Multiply -36 times -19.

$$x=\frac{0±\sqrt{684}}{2\times 9}$$

Take the square root of 684.

$$x=\frac{0±6\sqrt{19}}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{0±6\sqrt{19}}{18}$$

Now solve the equation x=\frac{0±6\sqrt{19}}{18} when ± is plus.

$$x=\frac{\sqrt{19}}{3}$$

Now solve the equation x=\frac{0±6\sqrt{19}}{18} when ± is minus.

$$x=-\frac{\sqrt{19}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{19}}{3} x=-\frac{\sqrt{19}}{3}$$