Solve x=frac{-bpmsqrt{b^2-49c}}{2a}

$$x = \frac { - b \pm \sqrt { b ^ { 2 } - 49 c } } { 2 a }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{-b±\sqrt{b^{2}-49c}}{2x}\text{, }&-b±\sqrt{b^{2}-49c}\neq 0\text{ and }x\neq 0\\a\neq 0\text{, }&x=0\text{ and }-b±\sqrt{b^{2}-49c}=0\end{matrix}\right.$$

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 2a.

$$x\times 2a=-b±\sqrt{b^{2}-49c}$$

Reorder the terms.

$$2ax=-b±\sqrt{b^{2}-49c}$$

The equation is in standard form.

$$2xa=-b±\sqrt{b^{2}-49c}$$

Divide both sides by 2x.

$$\frac{2xa}{2x}=\frac{-b±\sqrt{b^{2}-49c}}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$a=\frac{-b±\sqrt{b^{2}-49c}}{2x}$$

Variable a cannot be equal to 0.

$$a=\frac{-b±\sqrt{b^{2}-49c}}{2x}\text{, }a\neq 0$$

Solve for a

$$\left\{\begin{matrix}a=\frac{-b±\sqrt{b^{2}-49c}}{2x}\text{, }&-b±\sqrt{b^{2}-49c}\neq 0\text{ and }x\neq 0\text{ and }c\leq \frac{b^{2}}{49}\\a\neq 0\text{, }&c\leq \frac{b^{2}}{49}\text{ and }\left(c<0\text{ or }|b|\geq 7\sqrt{c}\right)\text{ and }x=0\text{ and }-b±\sqrt{b^{2}-49c}=0\end{matrix}\right.$$

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 2a.

$$x\times 2a=-b±\sqrt{b^{2}-49c}$$

Reorder the terms.

$$2ax=-b±\sqrt{b^{2}-49c}$$

The equation is in standard form.

$$2xa=-b±\sqrt{b^{2}-49c}$$

Divide both sides by 2x.

$$\frac{2xa}{2x}=\frac{-b±\sqrt{b^{2}-49c}}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$a=\frac{-b±\sqrt{b^{2}-49c}}{2x}$$

Variable a cannot be equal to 0.

$$a=\frac{-b±\sqrt{b^{2}-49c}}{2x}\text{, }a\neq 0$$