7v^2-36v+15=0

Solution for 7v^2-36v+15=0 equation:

7v^2-36v+15=0

a = 7; b = -36; c = +15;
Δ = b2-4ac
Δ = -362-4·7·15
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{219}}{2*7}=\frac{36-2\sqrt{219}}{14}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{219}}{2*7}=\frac{36+2\sqrt{219}}{14}
$