Løs -36.34=11.11Deltat-4.9Deltat^2

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

Løs for Δ

$$\Delta =-\frac{1817}{50t\left(-\frac{49t}{10}+11,11\right)}$$

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

Trinn for å løse lineære ligninger

Bytt om sidene, slik at alle variabelledd er på venstre side.

$$11,11\Delta t-4,9\Delta t^{2}=-36,34$$

Kombiner alle ledd som inneholder \Delta .

$$\left(11,11t-4,9t^{2}\right)\Delta =-36,34$$

Ligningen er i standardform.

$$\left(-\frac{49t^{2}}{10}+\frac{1111t}{100}\right)\Delta =-36,34$$

Del begge sidene på 11,11t-4,9t^{2}.

$$\frac{\left(-\frac{49t^{2}}{10}+\frac{1111t}{100}\right)\Delta }{-\frac{49t^{2}}{10}+\frac{1111t}{100}}=-\frac{36,34}{-\frac{49t^{2}}{10}+\frac{1111t}{100}}$$

Hvis du deler på 11,11t-4,9t^{2}, gjør du om gangingen med 11,11t-4,9t^{2}.

$$\Delta =-\frac{36,34}{-\frac{49t^{2}}{10}+\frac{1111t}{100}}$$

Del -36,34 på 11,11t-4,9t^{2}.

$$\Delta =-\frac{1817}{50t\left(-\frac{49t}{10}+11,11\right)}$$

Løs for t (complex solution)

$$t=\frac{5\left(\sqrt{\Delta \left(\frac{1234321\Delta }{10000}+712,264\right)}+\frac{1111\Delta }{100}\right)}{49\Delta }$$

$$t=\frac{-\frac{5\sqrt{\Delta \left(\frac{1234321\Delta }{10000}+712,264\right)}}{49}+\frac{1111\Delta }{980}}{\Delta }\text{, }\Delta \neq 0$$

Løs for t

$$t=\frac{5\left(\sqrt{\Delta \left(\frac{1234321\Delta }{10000}+712,264\right)}+\frac{1111\Delta }{100}\right)}{49\Delta }$$

$$t=\frac{-\frac{5\sqrt{\Delta \left(\frac{1234321\Delta }{10000}+712,264\right)}}{49}+\frac{1111\Delta }{980}}{\Delta }\text{, }\Delta >0\text{ or }\Delta \leq -\frac{7122640}{1234321}$$