Solve 0=100+3d-5t^2

$$0 = 100 + 3 d - 5 t ^ { 2 }$$

Solve for d

$$d=\frac{5\left(t^{2}-20\right)}{3}$$

Steps for Solving Linear Equation

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

$$100+3d-5t^{2}=0$$

Subtract 100 from both sides. Anything subtracted from zero gives its negation.

$$3d-5t^{2}=-100$$

Add 5t^{2} to both sides.

$$3d=-100+5t^{2}$$

The equation is in standard form.

$$3d=5t^{2}-100$$

Divide both sides by 3.

$$\frac{3d}{3}=\frac{5t^{2}-100}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$d=\frac{5t^{2}-100}{3}$$

Solve for t

$$t=\frac{\sqrt{15d+500}}{5}$$

$$t=-\frac{\sqrt{15d+500}}{5}\text{, }d\geq -\frac{100}{3}$$