Solve 3*10^5-2*10^5=2*10^4v^2/60

$$3 \times 10 ^ { 5 } - 2 \times 10 ^ { 5 } = \frac { 2 \times 10 ^ { 4 } v ^ { 2 } } { 60 }$$

Solve for v

$$v=10\sqrt{3}\approx 17.320508076$$

$$v=-10\sqrt{3}\approx -17.320508076$$

Steps by Finding Square Root

Multiply both sides of the equation by 60.

$$180\times 10^{5}-120\times 10^{5}=2\times 10^{4}v^{2}$$

Calculate 10 to the power of 5 and get 100000.

$$180\times 100000-120\times 10^{5}=2\times 10^{4}v^{2}$$

Multiply 180 and 100000 to get 18000000.

$$18000000-120\times 10^{5}=2\times 10^{4}v^{2}$$

Calculate 10 to the power of 5 and get 100000.

$$18000000-120\times 100000=2\times 10^{4}v^{2}$$

Multiply 120 and 100000 to get 12000000.

$$18000000-12000000=2\times 10^{4}v^{2}$$

Subtract 12000000 from 18000000 to get 6000000.

$$6000000=2\times 10^{4}v^{2}$$

Calculate 10 to the power of 4 and get 10000.

$$6000000=2\times 10000v^{2}$$

Multiply 2 and 10000 to get 20000.

$$6000000=20000v^{2}$$

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

$$20000v^{2}=6000000$$

Divide both sides by 20000.

$$v^{2}=\frac{6000000}{20000}$$

Divide 6000000 by 20000 to get 300.

$$v^{2}=300$$

Take the square root of both sides of the equation.

$$v=10\sqrt{3} v=-10\sqrt{3}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 60.

$$180\times 10^{5}-120\times 10^{5}=2\times 10^{4}v^{2}$$

Calculate 10 to the power of 5 and get 100000.

$$180\times 100000-120\times 10^{5}=2\times 10^{4}v^{2}$$

Multiply 180 and 100000 to get 18000000.

$$18000000-120\times 10^{5}=2\times 10^{4}v^{2}$$

Calculate 10 to the power of 5 and get 100000.

$$18000000-120\times 100000=2\times 10^{4}v^{2}$$

Multiply 120 and 100000 to get 12000000.

$$18000000-12000000=2\times 10^{4}v^{2}$$

Subtract 12000000 from 18000000 to get 6000000.

$$6000000=2\times 10^{4}v^{2}$$

Calculate 10 to the power of 4 and get 10000.

$$6000000=2\times 10000v^{2}$$

Multiply 2 and 10000 to get 20000.

$$6000000=20000v^{2}$$

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

$$20000v^{2}=6000000$$

Subtract 6000000 from both sides.

$$20000v^{2}-6000000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 20000 for a, 0 for b, and -6000000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\times 20000\left(-6000000\right)}}{2\times 20000}$$

Square 0.

$$v=\frac{0±\sqrt{-4\times 20000\left(-6000000\right)}}{2\times 20000}$$

Multiply -4 times 20000.

$$v=\frac{0±\sqrt{-80000\left(-6000000\right)}}{2\times 20000}$$

Multiply -80000 times -6000000.

$$v=\frac{0±\sqrt{480000000000}}{2\times 20000}$$

Take the square root of 480000000000.

$$v=\frac{0±400000\sqrt{3}}{2\times 20000}$$

Multiply 2 times 20000.

$$v=\frac{0±400000\sqrt{3}}{40000}$$

Now solve the equation v=\frac{0±400000\sqrt{3}}{40000} when ± is plus.

$$v=10\sqrt{3}$$

Now solve the equation v=\frac{0±400000\sqrt{3}}{40000} when ± is minus.

$$v=-10\sqrt{3}$$

The equation is now solved.

$$v=10\sqrt{3} v=-10\sqrt{3}$$