Solve A^2-3A-7I_{2}=O_{2}

$$A ^ { 2 } - 3 A - 7 I _ { 2 } = O _ { 2 }$$

Solve for I_2

$$I_{2}=\frac{A^{2}-3A-O_{2}}{7}$$

Steps for Solving Linear Equation

Subtract A^{2} from both sides.

$$-3A-7I_{2}=O_{2}-A^{2}$$

Add 3A to both sides.

$$-7I_{2}=O_{2}-A^{2}+3A$$

The equation is in standard form.

$$-7I_{2}=O_{2}+3A-A^{2}$$

Divide both sides by -7.

$$\frac{-7I_{2}}{-7}=\frac{O_{2}+3A-A^{2}}{-7}$$

Dividing by -7 undoes the multiplication by -7.

$$I_{2}=\frac{O_{2}+3A-A^{2}}{-7}$$

Divide O_{2}-A^{2}+3A by -7.

$$I_{2}=\frac{A^{2}-3A-O_{2}}{7}$$

Solve for A

$$A=\frac{\sqrt{28I_{2}+4O_{2}+9}+3}{2}$$

$$A=\frac{-\sqrt{28I_{2}+4O_{2}+9}+3}{2}\text{, }I_{2}\geq -\frac{O_{2}}{7}-\frac{9}{28}$$