Solve 6a^2+8b+6=0

$$6 a ^ { 2 } + 8 b + 6 = 0$$

Solve for b

$$b=\frac{-3a^{2}-3}{4}$$

Steps for Solving Linear Equation

Subtract 6a^{2} from both sides. Anything subtracted from zero gives its negation.

$$8b+6=-6a^{2}$$

Subtract 6 from both sides.

$$8b=-6a^{2}-6$$

Divide both sides by 8.

$$\frac{8b}{8}=\frac{-6a^{2}-6}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$b=\frac{-6a^{2}-6}{8}$$

Divide -6a^{2}-6 by 8.

$$b=\frac{-3a^{2}-3}{4}$$

Solve for a

$$a=\frac{\sqrt{-12b-9}}{3}$$

$$a=-\frac{\sqrt{-12b-9}}{3}\text{, }b\leq -\frac{3}{4}$$