Réitigh 0.12aT0.04(20-a)=20*0.09

$$0.12 a T 0.04 ( 20 - a ) = 20 \times 0.09$$

Réitigh do T_0.

$$T_{0}=-\frac{375}{a\left(a-20\right)}$$

$$a\neq 20\text{ and }a\neq 0$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Méadaigh 0.12 agus 0.04 chun 0.0048 a fháil.

$$0.0048aT_{0}\left(20-a\right)=20\times 0.09$$

Úsáid an t-airí dáileach chun 0.0048aT_{0} a mhéadú faoi 20-a.

$$0.096aT_{0}-0.0048a^{2}T_{0}=20\times 0.09$$

Méadaigh 20 agus 0.09 chun 1.8 a fháil.

$$0.096aT_{0}-0.0048a^{2}T_{0}=1.8$$

Comhcheangail na téarmaí ar fad ina bhfuil T_{0}.

$$\left(0.096a-0.0048a^{2}\right)T_{0}=1.8$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$\left(-\frac{3a^{2}}{625}+\frac{12a}{125}\right)T_{0}=1.8$$

Roinn an dá thaobh faoi 0.096a-0.0048a^{2}.

$$\frac{\left(-\frac{3a^{2}}{625}+\frac{12a}{125}\right)T_{0}}{-\frac{3a^{2}}{625}+\frac{12a}{125}}=\frac{1.8}{-\frac{3a^{2}}{625}+\frac{12a}{125}}$$

Má roinntear é faoi 0.096a-0.0048a^{2} cuirtear an iolrúchán faoi 0.096a-0.0048a^{2} ar ceal.

$$T_{0}=\frac{1.8}{-\frac{3a^{2}}{625}+\frac{12a}{125}}$$

Roinn 1.8 faoi 0.096a-0.0048a^{2}.

$$T_{0}=\frac{9}{5a\left(-\frac{3a}{625}+0.096\right)}$$

Réitigh do a. (complex solution)

$$a=-\frac{5\left(\sqrt{T_{0}\left(4T_{0}-15\right)}-2T_{0}\right)}{T_{0}}$$

$$a=\frac{5\left(\sqrt{T_{0}\left(4T_{0}-15\right)}+2T_{0}\right)}{T_{0}}\text{, }T_{0}\neq 0$$

Réitigh do a.

$$a=-\frac{5\left(\sqrt{T_{0}\left(4T_{0}-15\right)}-2T_{0}\right)}{T_{0}}$$

$$a=\frac{5\left(\sqrt{T_{0}\left(4T_{0}-15\right)}+2T_{0}\right)}{T_{0}}\text{, }T_{0}<0\text{ or }T_{0}\geq \frac{15}{4}$$