Solve 22*5=4*9t^2

$$22 \cdot 5 = 4 \cdot 9 t ^ { 2 }$$

Solve for t

$$t = \frac{\sqrt{110}}{6} \approx 1.748014747$$

$$t = -\frac{\sqrt{110}}{6} \approx -1.748014747$$

Steps by Finding Square Root

Multiply 22 and 5 to get 110.

$$110=4\times 9t^{2}$$

Multiply 4 and 9 to get 36.

$$110=36t^{2}$$

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

$$36t^{2}=110$$

Divide both sides by 36.

$$t^{2}=\frac{110}{36}$$

Reduce the fraction \frac{110}{36} to lowest terms by extracting and canceling out 2.

$$t^{2}=\frac{55}{18}$$

Take the square root of both sides of the equation.

$$t=\frac{\sqrt{110}}{6} t=-\frac{\sqrt{110}}{6}$$

Steps Using the Quadratic Formula

Multiply 22 and 5 to get 110.

$$110=4\times 9t^{2}$$

Multiply 4 and 9 to get 36.

$$110=36t^{2}$$

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

$$36t^{2}=110$$

Subtract 110 from both sides.

$$36t^{2}-110=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 36 for a, 0 for b, and -110 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times 36\left(-110\right)}}{2\times 36}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times 36\left(-110\right)}}{2\times 36}$$

Multiply -4 times 36.

$$t=\frac{0±\sqrt{-144\left(-110\right)}}{2\times 36}$$

Multiply -144 times -110.

$$t=\frac{0±\sqrt{15840}}{2\times 36}$$

Take the square root of 15840.

$$t=\frac{0±12\sqrt{110}}{2\times 36}$$

Multiply 2 times 36.

$$t=\frac{0±12\sqrt{110}}{72}$$

Now solve the equation t=\frac{0±12\sqrt{110}}{72} when ± is plus.

$$t=\frac{\sqrt{110}}{6}$$

Now solve the equation t=\frac{0±12\sqrt{110}}{72} when ± is minus.

$$t=-\frac{\sqrt{110}}{6}$$

The equation is now solved.

$$t=\frac{\sqrt{110}}{6} t=-\frac{\sqrt{110}}{6}$$