Whakaoti i te x/3*3+x/4*4+x/6*xs+(x/4-8)*2=504

$$\frac { x } { 3 } \times 3 + \frac { x } { 4 } \times 4 + \frac { x } { 6 } \cdot x s + ( \frac { x } { 4 } - 8 ) \cdot 2 = 504$$

Whakaoti mō s

$$s=-\frac{15\left(x-208\right)}{x^{2}}$$

$$x\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 12, arā, te tauraro pātahi he tino iti rawa te kitea o 3,4,6.

$$4x\times 3+3x\times 4+2xxs+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Whakareatia te x ki te x, ka x^{2}.

$$4x\times 3+3x\times 4+2x^{2}s+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Whakareatia te 4 ki te 3, ka 12.

$$12x+3x\times 4+2x^{2}s+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Whakareatia te 3 ki te 4, ka 12.

$$12x+12x+2x^{2}s+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Pahekotia te 12x me 12x, ka 24x.

$$24x+2x^{2}s+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Whakareatia te 12 ki te 2, ka 24.

$$24x+2x^{2}s+24\left(\frac{x}{4}-8\right)=6048$$

Whakamahia te āhuatanga tohatoha hei whakarea te 24 ki te \frac{x}{4}-8.

$$24x+2x^{2}s+24\times \frac{x}{4}-192=6048$$

Whakakorea atu te tauwehe pūnoa nui rawa 4 i roto i te 24 me te 4.

$$24x+2x^{2}s+6x-192=6048$$

Pahekotia te 24x me 6x, ka 30x.

$$30x+2x^{2}s-192=6048$$

Tangohia te 30x mai i ngā taha e rua.

$$2x^{2}s-192=6048-30x$$

Me tāpiri te 192 ki ngā taha e rua.

$$2x^{2}s=6048-30x+192$$

Tāpirihia te 6048 ki te 192, ka 6240.

$$2x^{2}s=6240-30x$$

Whakawehea ngā taha e rua ki te 2x^{2}.

$$\frac{2x^{2}s}{2x^{2}}=\frac{6240-30x}{2x^{2}}$$

Mā te whakawehe ki te 2x^{2} ka wetekia te whakareanga ki te 2x^{2}.

$$s=\frac{6240-30x}{2x^{2}}$$

Whakawehe 6240-30x ki te 2x^{2}.

$$s=\frac{15\left(208-x\right)}{x^{2}}$$

Whakaoti mō x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{15\left(832s+15\right)}-15}{2s}\text{; }x=-\frac{\sqrt{15}\left(\sqrt{832s+15}+\sqrt{15}\right)}{2s}\text{, }&s\neq 0\\x=208\text{, }&s=0\end{matrix}\right.$$

Whakaoti mō x

$$\left\{\begin{matrix}x=\frac{\sqrt{15\left(832s+15\right)}-15}{2s}\text{; }x=-\frac{\sqrt{15}\left(\sqrt{832s+15}+\sqrt{15}\right)}{2s}\text{, }&s\neq 0\text{ and }s\geq -\frac{15}{832}\\x=208\text{, }&s=0\end{matrix}\right.$$