Solve y^2+uy-27=0

$$y ^ { 2 } + u y - 27 = 0$$

Solve for u

$$u=-y+\frac{27}{y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Subtract y^{2} from both sides. Anything subtracted from zero gives its negation.

$$uy-27=-y^{2}$$

Add 27 to both sides.

$$uy=-y^{2}+27$$

The equation is in standard form.

$$yu=27-y^{2}$$

Divide both sides by y.

$$\frac{yu}{y}=\frac{27-y^{2}}{y}$$

Dividing by y undoes the multiplication by y.

$$u=\frac{27-y^{2}}{y}$$

Divide -y^{2}+27 by y.

$$u=-y+\frac{27}{y}$$

Solve for y

$$y=\frac{\sqrt{u^{2}+108}-u}{2}$$

$$y=\frac{-\sqrt{u^{2}+108}-u}{2}$$