Solve gt-delta/4(5t-1)=5t+5/8

$$g t - \frac { \delta } { 4 } ( 5 t - 1 ) = 5 t + \frac { 5 } { 8 }$$

Solve for g

$$\left\{\begin{matrix}g=\frac{5\delta }{4}-\frac{\delta }{4t}+5+\frac{5}{8t}\text{, }&t\neq 0\\g\in \mathrm{R}\text{, }&\delta =\frac{5}{2}\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8, the least common multiple of 4,8.

$$8gt-2\delta \left(5t-1\right)=40t+5$$

Add 2\delta \left(5t-1\right) to both sides.

$$8gt=40t+5+2\delta \left(5t-1\right)$$

Use the distributive property to multiply 2\delta by 5t-1.

$$8gt=40t+5+10\delta t-2\delta$$

The equation is in standard form.

$$8tg=10t\delta +40t-2\delta +5$$

Divide both sides by 8t.

$$\frac{8tg}{8t}=\frac{10t\delta +40t-2\delta +5}{8t}$$

Dividing by 8t undoes the multiplication by 8t.

$$g=\frac{10t\delta +40t-2\delta +5}{8t}$$

Divide 40t+5+10\delta t-2\delta by 8t.

$$g=\frac{5\delta }{4}+\frac{-\frac{\delta }{4}+\frac{5}{8}}{t}+5$$

Solve for t

$$\left\{\begin{matrix}t=-\frac{2\delta -5}{2\left(4g-5\delta -20\right)}\text{, }&g\neq \frac{5\delta }{4}+5\\t\in \mathrm{R}\text{, }&\delta =\frac{5}{2}\text{ and }g=\frac{65}{8}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8, the least common multiple of 4,8.

$$8gt-2\delta \left(5t-1\right)=40t+5$$

Subtract 40t from both sides.

$$8gt-2\delta \left(5t-1\right)-40t=5$$

Use the distributive property to multiply -2\delta by 5t-1.

$$8gt-10\delta t+2\delta -40t=5$$

Subtract 2\delta from both sides.

$$8gt-10\delta t-40t=5-2\delta$$

Combine all terms containing t.

$$\left(8g-10\delta -40\right)t=5-2\delta$$

Divide both sides by 8g-10\delta -40.

$$\frac{\left(8g-10\delta -40\right)t}{8g-10\delta -40}=\frac{5-2\delta }{8g-10\delta -40}$$

Dividing by 8g-10\delta -40 undoes the multiplication by 8g-10\delta -40.

$$t=\frac{5-2\delta }{8g-10\delta -40}$$

Divide 5-2\delta by 8g-10\delta -40.

$$t=\frac{5-2\delta }{2\left(4g-5\delta -20\right)}$$