Solve 12a^2-7ab+b=0

$$12 a ^ { 2 } - 7 a b + b = 0$$

Solve for b

$$b=-\frac{12a^{2}}{1-7a}$$

$$a\neq \frac{1}{7}$$

Steps for Solving Linear Equation

Subtract 12a^{2} from both sides. Anything subtracted from zero gives its negation.

$$-7ab+b=-12a^{2}$$

Combine all terms containing b.

$$\left(-7a+1\right)b=-12a^{2}$$

The equation is in standard form.

$$\left(1-7a\right)b=-12a^{2}$$

Divide both sides by -7a+1.

$$\frac{\left(1-7a\right)b}{1-7a}=-\frac{12a^{2}}{1-7a}$$

Dividing by -7a+1 undoes the multiplication by -7a+1.

$$b=-\frac{12a^{2}}{1-7a}$$

Solve for a

$$a=\frac{\sqrt{b\left(49b-48\right)}+7b}{24}$$

$$a=\frac{-\sqrt{b\left(49b-48\right)}+7b}{24}\text{, }b\geq \frac{48}{49}\text{ or }b\leq 0$$