Solve y=a^2+6b-4

$$y = a ^ { 2 } + 6 b - 4$$

Solve for b

$$b=\frac{y-a^{2}+4}{6}$$

Steps for Solving Linear Equation

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

$$a^{2}+6b-4=y$$

Subtract a^{2} from both sides.

$$6b-4=y-a^{2}$$

Add 4 to both sides.

$$6b=y-a^{2}+4$$

Divide both sides by 6.

$$\frac{6b}{6}=\frac{y-a^{2}+4}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$b=\frac{y-a^{2}+4}{6}$$

Divide y-a^{2}+4 by 6.

$$b=-\frac{a^{2}}{6}+\frac{y}{6}+\frac{2}{3}$$

Solve for a (complex solution)

$$a=-\sqrt{y-6b+4}$$

$$a=\sqrt{y-6b+4}$$

Solve for a

$$a=\sqrt{y-6b+4}$$

$$a=-\sqrt{y-6b+4}\text{, }y\geq -\left(4-6b\right)$$