Solve (14-3d)(14+3d)/(14-d)(14+d)=5/6

$$\frac { ( 14 - 3 d ) ( 14 + 3 d ) } { ( 14 - d ) ( 14 + d ) } = \frac { 5 } { 6 }$$

Solve for d

$$d=2$$

$$d=-2$$

Steps by Finding Square Root

Variable d cannot be equal to any of the values -14,14 since division by zero is not defined. Multiply both sides of the equation by 6\left(d-14\right)\left(d+14\right), the least common multiple of \left(14-d\right)\left(14+d\right),6.

$$-6\left(14-3d\right)\left(14+3d\right)=5\left(d-14\right)\left(d+14\right)$$

Use the distributive property to multiply -6 by 14-3d.

$$\left(-84+18d\right)\left(14+3d\right)=5\left(d-14\right)\left(d+14\right)$$

Use the distributive property to multiply -84+18d by 14+3d and combine like terms.

$$-1176+54d^{2}=5\left(d-14\right)\left(d+14\right)$$

Use the distributive property to multiply 5 by d-14.

$$-1176+54d^{2}=\left(5d-70\right)\left(d+14\right)$$

Use the distributive property to multiply 5d-70 by d+14 and combine like terms.

$$-1176+54d^{2}=5d^{2}-980$$

Subtract 5d^{2} from both sides.

$$-1176+54d^{2}-5d^{2}=-980$$

Combine 54d^{2} and -5d^{2} to get 49d^{2}.

$$-1176+49d^{2}=-980$$

Add 1176 to both sides.

$$49d^{2}=-980+1176$$

Add -980 and 1176 to get 196.

$$49d^{2}=196$$

Divide both sides by 49.

$$d^{2}=\frac{196}{49}$$

Divide 196 by 49 to get 4.

$$d^{2}=4$$

Take the square root of both sides of the equation.

$$d=2 d=-2$$

Steps Using the Quadratic Formula

Variable d cannot be equal to any of the values -14,14 since division by zero is not defined. Multiply both sides of the equation by 6\left(d-14\right)\left(d+14\right), the least common multiple of \left(14-d\right)\left(14+d\right),6.

$$-6\left(14-3d\right)\left(14+3d\right)=5\left(d-14\right)\left(d+14\right)$$

Use the distributive property to multiply -6 by 14-3d.

$$\left(-84+18d\right)\left(14+3d\right)=5\left(d-14\right)\left(d+14\right)$$

Use the distributive property to multiply -84+18d by 14+3d and combine like terms.

$$-1176+54d^{2}=5\left(d-14\right)\left(d+14\right)$$

Use the distributive property to multiply 5 by d-14.

$$-1176+54d^{2}=\left(5d-70\right)\left(d+14\right)$$

Use the distributive property to multiply 5d-70 by d+14 and combine like terms.

$$-1176+54d^{2}=5d^{2}-980$$

Subtract 5d^{2} from both sides.

$$-1176+54d^{2}-5d^{2}=-980$$

Combine 54d^{2} and -5d^{2} to get 49d^{2}.

$$-1176+49d^{2}=-980$$

Add 980 to both sides.

$$-1176+49d^{2}+980=0$$

Add -1176 and 980 to get -196.

$$-196+49d^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$49d^{2}-196=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 49 for a, 0 for b, and -196 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$d=\frac{0±\sqrt{0^{2}-4\times 49\left(-196\right)}}{2\times 49}$$

Square 0.

$$d=\frac{0±\sqrt{-4\times 49\left(-196\right)}}{2\times 49}$$

Multiply -4 times 49.

$$d=\frac{0±\sqrt{-196\left(-196\right)}}{2\times 49}$$

Multiply -196 times -196.

$$d=\frac{0±\sqrt{38416}}{2\times 49}$$

Take the square root of 38416.

$$d=\frac{0±196}{2\times 49}$$

Multiply 2 times 49.

$$d=\frac{0±196}{98}$$

Now solve the equation d=\frac{0±196}{98} when ± is plus. Divide 196 by 98.

$$d=2$$

Now solve the equation d=\frac{0±196}{98} when ± is minus. Divide -196 by 98.

$$d=-2$$

The equation is now solved.

$$d=2 d=-2$$