Solve 2a^2+3ab+7n^2=0

$$2 a ^ { 2 } + 3 a b + 7 n ^ { 2 } = 0$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{7n^{2}}{3a}-\frac{2a}{3}\text{, }&a\neq 0\\b\in \mathrm{R}\text{, }&a=0\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$3ab+7n^{2}=-2a^{2}$$

Subtract 7n^{2} from both sides.

$$3ab=-2a^{2}-7n^{2}$$

The equation is in standard form.

$$3ab=-7n^{2}-2a^{2}$$

Divide both sides by 3a.

$$\frac{3ab}{3a}=\frac{-7n^{2}-2a^{2}}{3a}$$

Dividing by 3a undoes the multiplication by 3a.

$$b=\frac{-7n^{2}-2a^{2}}{3a}$$

Divide -2a^{2}-7n^{2} by 3a.

$$b=-\frac{7n^{2}}{3a}-\frac{2a}{3}$$

Solve for a

$$a=\frac{\sqrt{9b^{2}-56n^{2}}-3b}{4}$$

$$a=\frac{-\sqrt{9b^{2}-56n^{2}}-3b}{4}\text{, }|b|\geq \frac{2\sqrt{14}|n|}{3}$$