Solve (lambda-8)(lambda-1)T=100

$$( \lambda - 8 ) ( \lambda - 1 ) T = 100$$

Solve for T

$$T=\frac{100}{\left(\lambda -8\right)\left(\lambda -1\right)}$$

$$\lambda \neq 1\text{ and }\lambda \neq 8$$

Steps for Solving Linear Equation

Use the distributive property to multiply \lambda -8 by \lambda -1 and combine like terms.

$$\left(\lambda ^{2}-9\lambda +8\right)T=100$$

Divide both sides by \lambda ^{2}-9\lambda +8.

$$\frac{\left(\lambda ^{2}-9\lambda +8\right)T}{\lambda ^{2}-9\lambda +8}=\frac{100}{\lambda ^{2}-9\lambda +8}$$

Dividing by \lambda ^{2}-9\lambda +8 undoes the multiplication by \lambda ^{2}-9\lambda +8.

$$T=\frac{100}{\lambda ^{2}-9\lambda +8}$$

Divide 100 by \lambda ^{2}-9\lambda +8.

$$T=\frac{100}{\left(\lambda -8\right)\left(\lambda -1\right)}$$

Solve for λ

$$\lambda =\frac{\sqrt{49T^{2}+400T}}{2T}+\frac{9}{2}$$

$$\lambda =-\frac{\sqrt{49T^{2}+400T}}{2T}+\frac{9}{2}\text{, }T>0\text{ or }T\leq -\frac{400}{49}$$