Solve 0=-8a^2+4*1/2*a*b-8

$$0 = - 8 a ^ { 2 } + 4 \cdot \frac { 1 } { 2 } \cdot a \cdot b - 8$$

Solve for b

$$b=4a+\frac{4}{a}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Multiply 4 and \frac{1}{2} to get 2.

$$0=-8a^{2}+2ab-8$$

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

$$-8a^{2}+2ab-8=0$$

Add 8a^{2} to both sides. Anything plus zero gives itself.

$$2ab-8=8a^{2}$$

Add 8 to both sides.

$$2ab=8a^{2}+8$$

Divide both sides by 2a.

$$\frac{2ab}{2a}=\frac{8a^{2}+8}{2a}$$

Dividing by 2a undoes the multiplication by 2a.

$$b=\frac{8a^{2}+8}{2a}$$

Divide 8a^{2}+8 by 2a.

$$b=4a+\frac{4}{a}$$

Solve for a (complex solution)

$$a=\frac{-\sqrt{b^{2}-64}+b}{8}$$

$$a=\frac{\sqrt{b^{2}-64}+b}{8}$$

Solve for a

$$a=\frac{-\sqrt{b^{2}-64}+b}{8}$$

$$a=\frac{\sqrt{b^{2}-64}+b}{8}\text{, }|b|\geq 8$$