Resolver x/3*3+x/4*4+x/6*xs+(x/4-8)*2=504

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

Resolver s

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

$$x\neq 0$$

Pasos para resolver unha ecuación lineal

Multiplica ambos lados da ecuación por 12, o mínimo común denominador de 3,4,6.

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

Multiplica x e x para obter x^{2}.

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

Multiplica 4 e 3 para obter 12.

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

Multiplica 3 e 4 para obter 12.

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

Combina 12x e 12x para obter 24x.

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

Multiplica 12 e 2 para obter 24.

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

Usa a propiedade distributiva para multiplicar 24 por \frac{x}{4}-8.

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

Descarta o máximo común divisor 4 en 24 e 4.

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

Combina 24x e 6x para obter 30x.

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

Resta 30x en ambos lados.

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

Engadir 192 en ambos lados.

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

Suma 6048 e 192 para obter 6240.

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

Divide ambos lados entre 2x^{2}.

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

A división entre 2x^{2} desfai a multiplicación por 2x^{2}.

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

Divide 6240-30x entre 2x^{2}.

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

Resolver x (complex solution)

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

Resolver x

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