Solve y=4ac-b^2/4a

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

Solve for a

$$\left\{\begin{matrix}a=-\frac{b^{2}}{4\left(y-c\right)}\text{, }&b\neq 0\text{ and }y\neq c\\a\neq 0\text{, }&b=0\text{ and }y=c\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4a.

$$y\times 4a=4ac-b^{2}$$

Subtract 4ac from both sides.

$$y\times 4a-4ac=-b^{2}$$

Combine all terms containing a.

$$\left(y\times 4-4c\right)a=-b^{2}$$

The equation is in standard form.

$$\left(4y-4c\right)a=-b^{2}$$

Divide both sides by 4y-4c.

$$\frac{\left(4y-4c\right)a}{4y-4c}=-\frac{b^{2}}{4y-4c}$$

Dividing by 4y-4c undoes the multiplication by 4y-4c.

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

Divide -b^{2} by 4y-4c.

$$a=-\frac{b^{2}}{4\left(y-c\right)}$$

Variable a cannot be equal to 0.

$$a=-\frac{b^{2}}{4\left(y-c\right)}\text{, }a\neq 0$$

Solve for b (complex solution)

$$b=-2\sqrt{a}\sqrt{c-y}$$

$$b=2\sqrt{a}\sqrt{c-y}\text{, }a\neq 0$$

Solve for b

$$b=2\sqrt{a\left(c-y\right)}$$

$$b=-2\sqrt{a\left(c-y\right)}\text{, }\left(a<0\text{ or }y\leq c\right)\text{ and }\left(a>0\text{ or }y\geq c\right)\text{ and }a\neq 0$$