Solve 2t*3t/2=450

$$\frac { 2 t \cdot 3 t } { 2 } = 450$$

Solve for t

$$t=5\sqrt{6}\approx 12.247448714$$

$$t=-5\sqrt{6}\approx -12.247448714$$

Steps by Finding Square Root

Multiply both sides by 2.

$$2t\times 3t=450\times 2$$

Cancel out 2 on both sides.

$$t\times 3t=450$$

Multiply t and t to get t^{2}.

$$t^{2}\times 3=450$$

Divide both sides by 3.

$$t^{2}=\frac{450}{3}$$

Divide 450 by 3 to get 150.

$$t^{2}=150$$

Take the square root of both sides of the equation.

$$t=5\sqrt{6} t=-5\sqrt{6}$$

Steps Using the Quadratic Formula

Multiply both sides by 2.

$$2t\times 3t=450\times 2$$

Cancel out 2 on both sides.

$$t\times 3t=450$$

Multiply t and t to get t^{2}.

$$t^{2}\times 3=450$$

Subtract 450 from both sides.

$$t^{2}\times 3-450=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$3t^{2}-450=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -450 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times 3\left(-450\right)}}{2\times 3}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times 3\left(-450\right)}}{2\times 3}$$

Multiply -4 times 3.

$$t=\frac{0±\sqrt{-12\left(-450\right)}}{2\times 3}$$

Multiply -12 times -450.

$$t=\frac{0±\sqrt{5400}}{2\times 3}$$

Take the square root of 5400.

$$t=\frac{0±30\sqrt{6}}{2\times 3}$$

Multiply 2 times 3.

$$t=\frac{0±30\sqrt{6}}{6}$$

Now solve the equation t=\frac{0±30\sqrt{6}}{6} when ± is plus.

$$t=5\sqrt{6}$$

Now solve the equation t=\frac{0±30\sqrt{6}}{6} when ± is minus.

$$t=-5\sqrt{6}$$

The equation is now solved.

$$t=5\sqrt{6} t=-5\sqrt{6}$$