Solve 4/R1.5/150+x=0.0745

$$\frac { 4 } { R } \frac { 1.5 } { 150 + x } = 0.0745$$

Solve for R

$$R=\frac{12000}{149\left(x+150\right)}$$

$$x\neq -150$$

Steps for Solving Linear Equation

Variable R cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by R\left(x+150\right), the least common multiple of R,150+x.

$$\left(x+150\right)\times 4\times \frac{1.5}{150+x}=0.0745R\left(x+150\right)$$

Use the distributive property to multiply x+150 by 4.

$$\left(4x+600\right)\times \frac{1.5}{150+x}=0.0745R\left(x+150\right)$$

Use the distributive property to multiply 4x+600 by \frac{1.5}{150+x}.

$$4x\times \frac{1.5}{150+x}+600\times \frac{1.5}{150+x}=0.0745R\left(x+150\right)$$

Use the distributive property to multiply 0.0745R by x+150.

$$4x\times \frac{1.5}{150+x}+600\times \frac{1.5}{150+x}=0.0745Rx+11.175R$$

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

$$0.0745Rx+11.175R=4x\times \frac{1.5}{150+x}+600\times \frac{1.5}{150+x}$$

Multiply both sides of the equation by x+150.

$$0.0745Rx\left(x+150\right)+11.175R\left(x+150\right)=4x\times 1.5+600\times 1.5$$

Use the distributive property to multiply 0.0745Rx by x+150.

$$0.0745Rx^{2}+11.175Rx+11.175R\left(x+150\right)=4x\times 1.5+600\times 1.5$$

Use the distributive property to multiply 11.175R by x+150.

$$0.0745Rx^{2}+11.175Rx+11.175Rx+1676.25R=4x\times 1.5+600\times 1.5$$

Combine 11.175Rx and 11.175Rx to get 22.35Rx.

$$0.0745Rx^{2}+22.35Rx+1676.25R=4x\times 1.5+600\times 1.5$$

Multiply 4 and 1.5 to get 6.

$$0.0745Rx^{2}+22.35Rx+1676.25R=6x+600\times 1.5$$

Multiply 600 and 1.5 to get 900.

$$0.0745Rx^{2}+22.35Rx+1676.25R=6x+900$$

Combine all terms containing R.

$$\left(0.0745x^{2}+22.35x+1676.25\right)R=6x+900$$

The equation is in standard form.

$$\left(\frac{149x^{2}}{2000}+\frac{447x}{20}+1676.25\right)R=6x+900$$

Divide both sides by 0.0745x^{2}+22.35x+1676.25.

$$\frac{\left(\frac{149x^{2}}{2000}+\frac{447x}{20}+1676.25\right)R}{\frac{149x^{2}}{2000}+\frac{447x}{20}+1676.25}=\frac{6x+900}{\frac{149x^{2}}{2000}+\frac{447x}{20}+1676.25}$$

Dividing by 0.0745x^{2}+22.35x+1676.25 undoes the multiplication by 0.0745x^{2}+22.35x+1676.25.

$$R=\frac{6x+900}{\frac{149x^{2}}{2000}+\frac{447x}{20}+1676.25}$$

Divide 900+6x by 0.0745x^{2}+22.35x+1676.25.

$$R=\frac{12000}{149\left(x+150\right)}$$

Variable R cannot be equal to 0.

$$R=\frac{12000}{149\left(x+150\right)}\text{, }R\neq 0$$

Solve for x

$$x=-150+\frac{12000}{149R}$$

$$R\neq 0$$