Whakaoti i te gt-delta/4(5t-1)=5t+5/8

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

Whakaoti mō g

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 8, arā, te tauraro pātahi he tino iti rawa te kitea o 4,8.

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

Me tāpiri te 2\delta \left(5t-1\right) ki ngā taha e rua.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2\delta ki te 5t-1.

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

He hanga arowhānui tō te whārite.

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

Whakawehea ngā taha e rua ki te 8t.

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

Mā te whakawehe ki te 8t ka wetekia te whakareanga ki te 8t.

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

Whakawehe 40t+5+10\delta t-2\delta ki te 8t.

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

Whakaoti mō t

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 8, arā, te tauraro pātahi he tino iti rawa te kitea o 4,8.

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

Tangohia te 40t mai i ngā taha e rua.

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

Whakamahia te āhuatanga tohatoha hei whakarea te -2\delta ki te 5t-1.

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

Tangohia te 2\delta mai i ngā taha e rua.

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

Pahekotia ngā kīanga tau katoa e whai ana i te t.

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

Whakawehea ngā taha e rua ki te 8g-10\delta -40.

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

Mā te whakawehe ki te 8g-10\delta -40 ka wetekia te whakareanga ki te 8g-10\delta -40.

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

Whakawehe 5-2\delta ki te 8g-10\delta -40.

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