Solve Deltat=frac{-6.4pmsqrt{(6.4)^2-4(-4.9)(1.2)}}{2(-4.9)}

$$\Delta t = \frac { - 6.4 \pm \sqrt { ( 6.4 ) ^ { 2 } - 4 ( - 4.9 ) ( 1.2 ) } } { 2 ( - 4.9 ) }$$

Solve for t

$$\left\{\begin{matrix}t=-\frac{5\left(-6.4±\frac{2\sqrt{403}}{5}\right)}{49\Delta }\text{, }&\Delta \neq 0\\t\in \mathrm{R}\text{, }&-6.4±\frac{2\sqrt{403}}{5}=0\text{ and }\Delta =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate 6.4 to the power of 2 and get 40.96.

$$\Delta t=\frac{-6.4±\sqrt{40.96-4\left(-4.9\right)\times 1.2}}{2\left(-4.9\right)}$$

Multiply 4 and -4.9 to get -19.6.

$$\Delta t=\frac{-6.4±\sqrt{40.96-\left(-19.6\times 1.2\right)}}{2\left(-4.9\right)}$$

Multiply -19.6 and 1.2 to get -23.52.

$$\Delta t=\frac{-6.4±\sqrt{40.96-\left(-23.52\right)}}{2\left(-4.9\right)}$$

The opposite of -23.52 is 23.52.

$$\Delta t=\frac{-6.4±\sqrt{40.96+23.52}}{2\left(-4.9\right)}$$

Add 40.96 and 23.52 to get 64.48.

$$\Delta t=\frac{-6.4±\sqrt{64.48}}{2\left(-4.9\right)}$$

Multiply 2 and -4.9 to get -9.8.

$$\Delta t=\frac{-6.4±\sqrt{64.48}}{-9.8}$$

The equation is in standard form.

$$\Delta t=-\frac{5\left(-6.4±\sqrt{64.48}\right)}{49}$$

Divide both sides by \Delta .

$$\frac{\Delta t}{\Delta }=-\frac{\frac{5\left(-6.4±\frac{2\sqrt{403}}{5}\right)}{49}}{\Delta }$$

Dividing by \Delta undoes the multiplication by \Delta .

$$t=-\frac{\frac{5\left(-6.4±\frac{2\sqrt{403}}{5}\right)}{49}}{\Delta }$$

Divide -\frac{5\left(-6.4±\frac{2\sqrt{403}}{5}\right)}{49} by \Delta .

$$t=-\frac{5\left(-6.4±\frac{2\sqrt{403}}{5}\right)}{49\Delta }$$

Solve for Δ

$$\left\{\begin{matrix}\Delta =-\frac{5\left(-6.4±\frac{2\sqrt{403}}{5}\right)}{49t}\text{, }&t\neq 0\\\Delta \in \mathrm{R}\text{, }&-6.4±\frac{2\sqrt{403}}{5}=0\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate 6.4 to the power of 2 and get 40.96.

$$\Delta t=\frac{-6.4±\sqrt{40.96-4\left(-4.9\right)\times 1.2}}{2\left(-4.9\right)}$$

Multiply 4 and -4.9 to get -19.6.

$$\Delta t=\frac{-6.4±\sqrt{40.96-\left(-19.6\times 1.2\right)}}{2\left(-4.9\right)}$$

Multiply -19.6 and 1.2 to get -23.52.

$$\Delta t=\frac{-6.4±\sqrt{40.96-\left(-23.52\right)}}{2\left(-4.9\right)}$$

The opposite of -23.52 is 23.52.

$$\Delta t=\frac{-6.4±\sqrt{40.96+23.52}}{2\left(-4.9\right)}$$

Add 40.96 and 23.52 to get 64.48.

$$\Delta t=\frac{-6.4±\sqrt{64.48}}{2\left(-4.9\right)}$$

Multiply 2 and -4.9 to get -9.8.

$$\Delta t=\frac{-6.4±\sqrt{64.48}}{-9.8}$$

The equation is in standard form.

$$t\Delta =-\frac{5\left(-6.4±\sqrt{64.48}\right)}{49}$$

Divide both sides by t.

$$\frac{t\Delta }{t}=-\frac{\frac{5\left(-6.4±\frac{2\sqrt{403}}{5}\right)}{49}}{t}$$

Dividing by t undoes the multiplication by t.

$$\Delta =-\frac{\frac{5\left(-6.4±\frac{2\sqrt{403}}{5}\right)}{49}}{t}$$

Divide -\frac{5\left(-6.4±\frac{2\sqrt{403}}{5}\right)}{49} by t.

$$\Delta =-\frac{5\left(-6.4±\frac{2\sqrt{403}}{5}\right)}{49t}$$