Solve (6a+1)(7a-1)=a

$$( 6 a + 1 ) ( 7 a - 1 ) = a$$

Solve for a

$$a=\frac{\sqrt{42}}{42}\approx 0.15430335$$

$$a=-\frac{\sqrt{42}}{42}\approx -0.15430335$$

Steps by Finding Square Root

Use the distributive property to multiply 6a+1 by 7a-1 and combine like terms.

$$42a^{2}+a-1=a$$

Subtract a from both sides.

$$42a^{2}+a-1-a=0$$

Combine a and -a to get 0.

$$42a^{2}-1=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$42a^{2}=1$$

Divide both sides by 42.

$$a^{2}=\frac{1}{42}$$

Take the square root of both sides of the equation.

$$a=\frac{\sqrt{42}}{42} a=-\frac{\sqrt{42}}{42}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 6a+1 by 7a-1 and combine like terms.

$$42a^{2}+a-1=a$$

Subtract a from both sides.

$$42a^{2}+a-1-a=0$$

Combine a and -a to get 0.

$$42a^{2}-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 42 for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 42\left(-1\right)}}{2\times 42}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 42\left(-1\right)}}{2\times 42}$$

Multiply -4 times 42.

$$a=\frac{0±\sqrt{-168\left(-1\right)}}{2\times 42}$$

Multiply -168 times -1.

$$a=\frac{0±\sqrt{168}}{2\times 42}$$

Take the square root of 168.

$$a=\frac{0±2\sqrt{42}}{2\times 42}$$

Multiply 2 times 42.

$$a=\frac{0±2\sqrt{42}}{84}$$

Now solve the equation a=\frac{0±2\sqrt{42}}{84} when ± is plus.

$$a=\frac{\sqrt{42}}{42}$$

Now solve the equation a=\frac{0±2\sqrt{42}}{84} when ± is minus.

$$a=-\frac{\sqrt{42}}{42}$$

The equation is now solved.

$$a=\frac{\sqrt{42}}{42} a=-\frac{\sqrt{42}}{42}$$