Solve (85-30)(85+36)/(85-b)(85+b)=11/20

$$\frac { ( 85 - 30 ) ( 85 + 36 ) } { ( 85 - b ) ( 85 + b ) } = \frac { 11 } { 20 }$$

Solve for b

$$b=-5\sqrt{195}i\approx -0-69.821200219i$$

$$b=5\sqrt{195}i\approx 69.821200219i$$

Steps by Finding Square Root

Variable b cannot be equal to any of the values -85,85 since division by zero is not defined. Multiply both sides of the equation by 20\left(b-85\right)\left(b+85\right), the least common multiple of \left(85-b\right)\left(85+b\right),20.

$$-20\left(85-30\right)\left(85+36\right)=11\left(b-85\right)\left(b+85\right)$$

Subtract 30 from 85 to get 55.

$$-20\times 55\left(85+36\right)=11\left(b-85\right)\left(b+85\right)$$

Multiply -20 and 55 to get -1100.

$$-1100\left(85+36\right)=11\left(b-85\right)\left(b+85\right)$$

Add 85 and 36 to get 121.

$$-1100\times 121=11\left(b-85\right)\left(b+85\right)$$

Multiply -1100 and 121 to get -133100.

$$-133100=11\left(b-85\right)\left(b+85\right)$$

Use the distributive property to multiply 11 by b-85.

$$-133100=\left(11b-935\right)\left(b+85\right)$$

Use the distributive property to multiply 11b-935 by b+85 and combine like terms.

$$-133100=11b^{2}-79475$$

Swap sides so that all variable terms are on the left hand side.

$$11b^{2}-79475=-133100$$

Add 79475 to both sides.

$$11b^{2}=-133100+79475$$

Add -133100 and 79475 to get -53625.

$$11b^{2}=-53625$$

Divide both sides by 11.

$$b^{2}=\frac{-53625}{11}$$

Divide -53625 by 11 to get -4875.

$$b^{2}=-4875$$

The equation is now solved.

$$b=5\sqrt{195}i b=-5\sqrt{195}i$$

Steps Using the Quadratic Formula

Variable b cannot be equal to any of the values -85,85 since division by zero is not defined. Multiply both sides of the equation by 20\left(b-85\right)\left(b+85\right), the least common multiple of \left(85-b\right)\left(85+b\right),20.

$$-20\left(85-30\right)\left(85+36\right)=11\left(b-85\right)\left(b+85\right)$$

Subtract 30 from 85 to get 55.

$$-20\times 55\left(85+36\right)=11\left(b-85\right)\left(b+85\right)$$

Multiply -20 and 55 to get -1100.

$$-1100\left(85+36\right)=11\left(b-85\right)\left(b+85\right)$$

Add 85 and 36 to get 121.

$$-1100\times 121=11\left(b-85\right)\left(b+85\right)$$

Multiply -1100 and 121 to get -133100.

$$-133100=11\left(b-85\right)\left(b+85\right)$$

Use the distributive property to multiply 11 by b-85.

$$-133100=\left(11b-935\right)\left(b+85\right)$$

Use the distributive property to multiply 11b-935 by b+85 and combine like terms.

$$-133100=11b^{2}-79475$$

Swap sides so that all variable terms are on the left hand side.

$$11b^{2}-79475=-133100$$

Add 133100 to both sides.

$$11b^{2}-79475+133100=0$$

Add -79475 and 133100 to get 53625.

$$11b^{2}+53625=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 11 for a, 0 for b, and 53625 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\times 11\times 53625}}{2\times 11}$$

Square 0.

$$b=\frac{0±\sqrt{-4\times 11\times 53625}}{2\times 11}$$

Multiply -4 times 11.

$$b=\frac{0±\sqrt{-44\times 53625}}{2\times 11}$$

Multiply -44 times 53625.

$$b=\frac{0±\sqrt{-2359500}}{2\times 11}$$

Take the square root of -2359500.

$$b=\frac{0±110\sqrt{195}i}{2\times 11}$$

Multiply 2 times 11.

$$b=\frac{0±110\sqrt{195}i}{22}$$

Now solve the equation b=\frac{0±110\sqrt{195}i}{22} when ± is plus.

$$b=5\sqrt{195}i$$

Now solve the equation b=\frac{0±110\sqrt{195}i}{22} when ± is minus.

$$b=-5\sqrt{195}i$$

The equation is now solved.

$$b=5\sqrt{195}i b=-5\sqrt{195}i$$