Solve 1,375=6t-2t_2^2

$$1,375 = 6 t - 2 t _ { 2 } ^ { 2 }$$

Solve for t

$$t=\frac{t_{2}^{2}}{3}+\frac{1375}{6}$$

Steps for Solving Linear Equation

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

$$6t-2t_{2}^{2}=1375$$

Add 2t_{2}^{2} to both sides.

$$6t=1375+2t_{2}^{2}$$

The equation is in standard form.

$$6t=2t_{2}^{2}+1375$$

Divide both sides by 6.

$$\frac{6t}{6}=\frac{2t_{2}^{2}+1375}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$t=\frac{2t_{2}^{2}+1375}{6}$$

Divide 1375+2t_{2}^{2} by 6.

$$t=\frac{t_{2}^{2}}{3}+\frac{1375}{6}$$

Solve for t_2 (complex solution)

$$t_{2}=-\frac{\sqrt{12t-2750}}{2}$$

$$t_{2}=\frac{\sqrt{12t-2750}}{2}$$

Solve for t_2

$$t_{2}=\frac{\sqrt{12t-2750}}{2}$$

$$t_{2}=-\frac{\sqrt{12t-2750}}{2}\text{, }t\geq \frac{1375}{6}$$