Solve 39=frac{a^2+bsqrt{3*9^2*8}}{29x}

$$39 = \frac { a ^ { 2 } + b \sqrt { 3 \times 9 ^ { 2 } \times 8 } } { 29 x }$$

Solve for b

$$b=-\frac{\sqrt{6}\left(a^{2}-1131x\right)}{108}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 29x.

$$1131x=a^{2}+b\sqrt{3\times 9^{2}\times 8}$$

Calculate 9 to the power of 2 and get 81.

$$1131x=a^{2}+b\sqrt{3\times 81\times 8}$$

Multiply 3 and 81 to get 243.

$$1131x=a^{2}+b\sqrt{243\times 8}$$

Multiply 243 and 8 to get 1944.

$$1131x=a^{2}+b\sqrt{1944}$$

Factor 1944=18^{2}\times 6. Rewrite the square root of the product \sqrt{18^{2}\times 6} as the product of square roots \sqrt{18^{2}}\sqrt{6}. Take the square root of 18^{2}.

$$1131x=a^{2}+b\times 18\sqrt{6}$$

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

$$a^{2}+b\times 18\sqrt{6}=1131x$$

Subtract a^{2} from both sides.

$$b\times 18\sqrt{6}=1131x-a^{2}$$

The equation is in standard form.

$$18\sqrt{6}b=1131x-a^{2}$$

Divide both sides by 18\sqrt{6}.

$$\frac{18\sqrt{6}b}{18\sqrt{6}}=\frac{1131x-a^{2}}{18\sqrt{6}}$$

Dividing by 18\sqrt{6} undoes the multiplication by 18\sqrt{6}.

$$b=\frac{1131x-a^{2}}{18\sqrt{6}}$$

Divide 1131x-a^{2} by 18\sqrt{6}.

$$b=\frac{\sqrt{6}\left(1131x-a^{2}\right)}{108}$$

Solve for a (complex solution)

$$a=-\sqrt{-18\sqrt{6}b+1131x}$$

$$a=\sqrt{-18\sqrt{6}b+1131x}\text{, }x\neq 0$$

Solve for a

$$a=\sqrt{-18\sqrt{6}b+1131x}$$

$$a=-\sqrt{-18\sqrt{6}b+1131x}\text{, }b\leq \frac{377\sqrt{6}x}{36}\text{ and }x\neq 0$$