Solve -36.34=11.11Deltat-4.9Deltat^2

$$- 36.34 = 11.11 \Delta t - 4.9 \Delta t ^ { 2 }$$

Solve for Δ

$$\Delta =-\frac{1817}{50t\left(-\frac{49t}{10}+11.11\right)}$$

$$t\neq \frac{1111}{490}\text{ and }t\neq 0$$

Steps for Solving Linear Equation

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

$$11.11\Delta t-4.9\Delta t^{2}=-36.34$$

Combine all terms containing \Delta .

$$\left(11.11t-4.9t^{2}\right)\Delta =-36.34$$

The equation is in standard form.

$$\left(-\frac{49t^{2}}{10}+\frac{1111t}{100}\right)\Delta =-36.34$$

Divide both sides by 11.11t-4.9t^{2}.

$$\frac{\left(-\frac{49t^{2}}{10}+\frac{1111t}{100}\right)\Delta }{-\frac{49t^{2}}{10}+\frac{1111t}{100}}=-\frac{36.34}{-\frac{49t^{2}}{10}+\frac{1111t}{100}}$$

Dividing by 11.11t-4.9t^{2} undoes the multiplication by 11.11t-4.9t^{2}.

$$\Delta =-\frac{36.34}{-\frac{49t^{2}}{10}+\frac{1111t}{100}}$$

Divide -36.34 by 11.11t-4.9t^{2}.

$$\Delta =-\frac{1817}{50t\left(-\frac{49t}{10}+11.11\right)}$$

Solve for t (complex solution)

$$t=\frac{5\left(\sqrt{\Delta \left(\frac{1234321\Delta }{10000}+712.264\right)}+\frac{1111\Delta }{100}\right)}{49\Delta }$$

$$t=\frac{-\frac{5\sqrt{\Delta \left(\frac{1234321\Delta }{10000}+712.264\right)}}{49}+\frac{1111\Delta }{980}}{\Delta }\text{, }\Delta \neq 0$$

Solve for t

$$t=\frac{5\left(\sqrt{\Delta \left(\frac{1234321\Delta }{10000}+712.264\right)}+\frac{1111\Delta }{100}\right)}{49\Delta }$$

$$t=\frac{-\frac{5\sqrt{\Delta \left(\frac{1234321\Delta }{10000}+712.264\right)}}{49}+\frac{1111\Delta }{980}}{\Delta }\text{, }\Delta >0\text{ or }\Delta \leq -\frac{7122640}{1234321}$$