Solve 19xdiv3x=3

$$19x \div 3x=3$$

Solve for x

$$x=\frac{3\sqrt{19}}{19}\approx 0.688247202$$

$$x=-\frac{3\sqrt{19}}{19}\approx -0.688247202$$

Steps by Finding Square Root

Multiply both sides of the equation by 3.

$$19xx=9$$

Multiply x and x to get x^{2}.

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

Divide both sides by 19.

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

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Multiply both sides of the equation by 3.

$$19xx=9$$

Multiply x and x to get x^{2}.

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

Subtract 9 from both sides.

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

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

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

Square 0.

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

Multiply -4 times 19.

$$x=\frac{0±\sqrt{-76\left(-9\right)}}{2\times 19}$$

Multiply -76 times -9.

$$x=\frac{0±\sqrt{684}}{2\times 19}$$

Take the square root of 684.

$$x=\frac{0±6\sqrt{19}}{2\times 19}$$

Multiply 2 times 19.

$$x=\frac{0±6\sqrt{19}}{38}$$

Now solve the equation x=\frac{0±6\sqrt{19}}{38} when ± is plus.

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

Now solve the equation x=\frac{0±6\sqrt{19}}{38} when ± is minus.

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

The equation is now solved.

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