Solve y+4y=(Deltax+x^2)+1

$$y + 4 y = ( \Delta x + x ^ { 2 } ) + 1$$

Solve for y

$$y=\frac{x^{2}+x\Delta +1}{5}$$

Steps for Solving Linear Equation

Combine y and 4y to get 5y.

$$5y=\Delta x+x^{2}+1$$

The equation is in standard form.

$$5y=x^{2}+x\Delta +1$$

Divide both sides by 5.

$$\frac{5y}{5}=\frac{x^{2}+x\Delta +1}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$y=\frac{x^{2}+x\Delta +1}{5}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{20y+\Delta ^{2}-4}-\Delta }{2}$$

$$x=\frac{-\sqrt{20y+\Delta ^{2}-4}-\Delta }{2}$$

Solve for x

$$x=\frac{\sqrt{20y+\Delta ^{2}-4}-\Delta }{2}$$

$$x=\frac{-\sqrt{20y+\Delta ^{2}-4}-\Delta }{2}\text{, }y\geq -\frac{\Delta ^{2}}{20}+\frac{1}{5}$$