Solve y=1/2x^2-5t

$$y = \frac { 1 } { 2 } x ^ { 2 } - 5 t$$

Solve for t

$$t=\frac{x^{2}-2y}{10}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{2}x^{2}-5t=y$$

Subtract \frac{1}{2}x^{2} from both sides.

$$-5t=y-\frac{1}{2}x^{2}$$

The equation is in standard form.

$$-5t=-\frac{x^{2}}{2}+y$$

Divide both sides by -5.

$$\frac{-5t}{-5}=\frac{-\frac{x^{2}}{2}+y}{-5}$$

Dividing by -5 undoes the multiplication by -5.

$$t=\frac{-\frac{x^{2}}{2}+y}{-5}$$

Divide y-\frac{x^{2}}{2} by -5.

$$t=\frac{x^{2}}{10}-\frac{y}{5}$$

Solve for x (complex solution)

$$x=-\sqrt{2\left(y+5t\right)}$$

$$x=\sqrt{2\left(y+5t\right)}$$

Solve for x

$$x=\sqrt{2\left(y+5t\right)}$$

$$x=-\sqrt{2\left(y+5t\right)}\text{, }y\geq -5t$$