Solve -b^2x^2+ax+4=0

$$- b ^ { 2 } x ^ { 2 } + a x + 4 = 0$$

Solve for a

$$a=\frac{\left(bx\right)^{2}-4}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract \left(-b^{2}\right)x^{2} from both sides. Anything subtracted from zero gives its negation.

$$ax+4=-\left(-b^{2}\right)x^{2}$$

Subtract 4 from both sides.

$$ax=-\left(-b^{2}\right)x^{2}-4$$

Multiply -1 and -1 to get 1.

$$ax=b^{2}x^{2}-4$$

The equation is in standard form.

$$xa=b^{2}x^{2}-4$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{b^{2}x^{2}-4}{x}$$

Dividing by x undoes the multiplication by x.

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

Divide b^{2}x^{2}-4 by x.

$$a=xb^{2}-\frac{4}{x}$$

Solve for b (complex solution)

$$b=-\frac{\sqrt{ax+4}}{x}$$

$$b=\frac{\sqrt{ax+4}}{x}\text{, }x\neq 0$$

Solve for b

$$b=\frac{\sqrt{ax+4}}{|x|}$$

$$b=-\frac{\sqrt{ax+4}}{|x|}\text{, }\left(a\neq 0\text{ and }x=-\frac{4}{a}\right)\text{ or }\left(x\leq -\frac{4}{a}\text{ and }a\leq 0\text{ and }x\neq 0\right)\text{ or }\left(a\geq 0\text{ and }x\geq -\frac{4}{a}\text{ and }x\neq 0\right)\text{ or }\left(a=0\text{ and }x\neq 0\right)$$