v^2/120=25

Solution for v^2/120=25 equation:

v^2/120=25

We move all terms to the left:

v^2/120-(25)=0

We multiply all the terms by the denominator


v^2-25*120=0

We add all the numbers together, and all the variables

v^2-3000=0

a = 1; b = 0; c = -3000;
Δ = b2-4ac
Δ = 02-4·1·(-3000)
Δ = 12000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12000}=\sqrt{400*30}=\sqrt{400}*\sqrt{30}=20\sqrt{30}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{30}}{2*1}=\frac{0-20\sqrt{30}}{2}
=-\frac{20\sqrt{30}}{2}
=-10\sqrt{30}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{30}}{2*1}=\frac{0+20\sqrt{30}}{2}
=\frac{20\sqrt{30}}{2}
=10\sqrt{30}
$