Solve 4a^2+ab=-168+56a

$$4 a ^ { 2 } + a b = - 168 + 56 a$$

Solve for b

$$b=-4a+56-\frac{168}{a}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Subtract 4a^{2} from both sides.

$$ab=-168+56a-4a^{2}$$

The equation is in standard form.

$$ab=-4a^{2}+56a-168$$

Divide both sides by a.

$$\frac{ab}{a}=\frac{-4a^{2}+56a-168}{a}$$

Dividing by a undoes the multiplication by a.

$$b=\frac{-4a^{2}+56a-168}{a}$$

Divide -168+56a-4a^{2} by a.

$$b=-4a+56-\frac{168}{a}$$

Solve for a

$$a=\frac{\sqrt{b^{2}-112b+448}}{8}-\frac{b}{8}+7$$

$$a=-\frac{\sqrt{b^{2}-112b+448}}{8}-\frac{b}{8}+7\text{, }b\geq 8\sqrt{42}+56\text{ or }b\leq 56-8\sqrt{42}$$