Solve 20x^2-7-6=0

$$20 x ^ { 2 } - 7 - 6 = 0$$

Solve for x

$$x=\frac{\sqrt{65}}{10}\approx 0.806225775$$

$$x=-\frac{\sqrt{65}}{10}\approx -0.806225775$$

Steps by Finding Square Root

Subtract 6 from -7 to get -13.

$$20x^{2}-13=0$$

Add 13 to both sides. Anything plus zero gives itself.

$$20x^{2}=13$$

Divide both sides by 20.

$$x^{2}=\frac{13}{20}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{65}}{10} x=-\frac{\sqrt{65}}{10}$$

Steps Using the Quadratic Formula

Subtract 6 from -7 to get -13.

$$20x^{2}-13=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 20 for a, 0 for b, and -13 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 20\left(-13\right)}}{2\times 20}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 20\left(-13\right)}}{2\times 20}$$

Multiply -4 times 20.

$$x=\frac{0±\sqrt{-80\left(-13\right)}}{2\times 20}$$

Multiply -80 times -13.

$$x=\frac{0±\sqrt{1040}}{2\times 20}$$

Take the square root of 1040.

$$x=\frac{0±4\sqrt{65}}{2\times 20}$$

Multiply 2 times 20.

$$x=\frac{0±4\sqrt{65}}{40}$$

Now solve the equation x=\frac{0±4\sqrt{65}}{40} when ± is plus.

$$x=\frac{\sqrt{65}}{10}$$

Now solve the equation x=\frac{0±4\sqrt{65}}{40} when ± is minus.

$$x=-\frac{\sqrt{65}}{10}$$

The equation is now solved.

$$x=\frac{\sqrt{65}}{10} x=-\frac{\sqrt{65}}{10}$$