Solve 99/8a+2=x-999a/25

$$\frac{ 99 }{ 8a+2 } = \frac{ x-999a }{ 25 }$$

Solve for x

$$x=\frac{9\left(888a^{2}+222a+275\right)}{2\left(4a+1\right)}$$

$$a\neq -\frac{1}{4}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 50\left(4a+1\right), the least common multiple of 8a+2,25.

$$25\times 99=\left(8a+2\right)\left(x-999a\right)$$

Multiply 25 and 99 to get 2475.

$$2475=\left(8a+2\right)\left(x-999a\right)$$

Use the distributive property to multiply 8a+2 by x-999a.

$$2475=8ax-7992a^{2}+2x-1998a$$

Swap sides so that all variable terms are on the left hand side.

$$8ax-7992a^{2}+2x-1998a=2475$$

Add 7992a^{2} to both sides.

$$8ax+2x-1998a=2475+7992a^{2}$$

Add 1998a to both sides.

$$8ax+2x=2475+7992a^{2}+1998a$$

Combine all terms containing x.

$$\left(8a+2\right)x=2475+7992a^{2}+1998a$$

The equation is in standard form.

$$\left(8a+2\right)x=7992a^{2}+1998a+2475$$

Divide both sides by 8a+2.

$$\frac{\left(8a+2\right)x}{8a+2}=\frac{7992a^{2}+1998a+2475}{8a+2}$$

Dividing by 8a+2 undoes the multiplication by 8a+2.

$$x=\frac{7992a^{2}+1998a+2475}{8a+2}$$

Divide 2475+7992a^{2}+1998a by 8a+2.

$$x=\frac{9\left(888a^{2}+222a+275\right)}{2\left(4a+1\right)}$$

Solve for a (complex solution)

$$a=\frac{\sqrt{16x^{2}+7992x-18782199}}{7992}+\frac{x}{1998}-\frac{1}{8}$$

$$a=-\frac{\sqrt{16x^{2}+7992x-18782199}}{7992}+\frac{x}{1998}-\frac{1}{8}$$

Solve for a

$$a=\frac{\sqrt{16x^{2}+7992x-18782199}}{7992}+\frac{x}{1998}-\frac{1}{8}$$

$$a=-\frac{\sqrt{16x^{2}+7992x-18782199}}{7992}+\frac{x}{1998}-\frac{1}{8}\text{, }x\geq \frac{45\sqrt{2442}}{2}-\frac{999}{4}\text{ or }x\leq -\frac{45\sqrt{2442}}{2}-\frac{999}{4}$$