Solve x^2-5xy-3b=y^2

$$x ^ { 2 } - 5 x y - 3 b = y ^ { 2 }$$

Solve for b

$$b=\frac{x^{2}-5xy-y^{2}}{3}$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides.

$$-5xy-3b=y^{2}-x^{2}$$

Add 5xy to both sides.

$$-3b=y^{2}-x^{2}+5xy$$

The equation is in standard form.

$$-3b=y^{2}+5xy-x^{2}$$

Divide both sides by -3.

$$\frac{-3b}{-3}=\frac{y^{2}+5xy-x^{2}}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$b=\frac{y^{2}+5xy-x^{2}}{-3}$$

Divide y^{2}-x^{2}+5xy by -3.

$$b=\frac{x^{2}-5xy-y^{2}}{3}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{29y^{2}+12b}+5y}{2}$$

$$x=\frac{-\sqrt{29y^{2}+12b}+5y}{2}$$

Solve for x

$$x=\frac{\sqrt{29y^{2}+12b}+5y}{2}$$

$$x=\frac{-\sqrt{29y^{2}+12b}+5y}{2}\text{, }b\geq -\frac{29y^{2}}{12}$$