3v^2/20-14v+265=0

Solution for 3v^2/20-14v+265=0 equation:

3v^2/20-14v+265=0

We multiply all the terms by the denominator


3v^2-14v*20+265*20=0

We add all the numbers together, and all the variables

3v^2-14v*20+5300=0

Wy multiply elements

3v^2-280v+5300=0

a = 3; b = -280; c = +5300;
Δ = b2-4ac
Δ = -2802-4·3·5300
Δ = 14800
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:

$\sqrt{\Delta}=\sqrt{14800}=\sqrt{400*37}=\sqrt{400}*\sqrt{37}=20\sqrt{37}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-280)-20\sqrt{37}}{2*3}=\frac{280-20\sqrt{37}}{6}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-280)+20\sqrt{37}}{2*3}=\frac{280+20\sqrt{37}}{6}
$