Solve -16(52-DB^2)=48(20-DB^2)

$$- 16 ( 52 - D B ^ { 2 } ) = 48 ( 20 - D B ^ { 2 } )$$

Solve for D

$$D=\frac{28}{B^{2}}$$

$$B\neq 0$$

Steps for Solving Linear Equation

Subtract 48\left(20-DB^{2}\right) from both sides.

$$-16\left(52-DB^{2}\right)-48\left(20-DB^{2}\right)=0$$

Use the distributive property to multiply -16 by 52-DB^{2}.

$$-832+16DB^{2}-48\left(20-DB^{2}\right)=0$$

Use the distributive property to multiply -48 by 20-DB^{2}.

$$-832+16DB^{2}-960+48DB^{2}=0$$

Subtract 960 from -832 to get -1792.

$$-1792+16DB^{2}+48DB^{2}=0$$

Combine 16DB^{2} and 48DB^{2} to get 64DB^{2}.

$$-1792+64DB^{2}=0$$

Add 1792 to both sides. Anything plus zero gives itself.

$$64DB^{2}=1792$$

The equation is in standard form.

$$64B^{2}D=1792$$

Divide both sides by 64B^{2}.

$$\frac{64B^{2}D}{64B^{2}}=\frac{1792}{64B^{2}}$$

Dividing by 64B^{2} undoes the multiplication by 64B^{2}.

$$D=\frac{1792}{64B^{2}}$$

Divide 1792 by 64B^{2}.

$$D=\frac{28}{B^{2}}$$

Solve for B

$$B=2\sqrt{\frac{7}{D}}$$

$$B=-2\sqrt{\frac{7}{D}}\text{, }D>0$$