4v2+6v=65

Solution for 4v2+6v=65 equation:

4v^2+6v=65

We move all terms to the left:

4v^2+6v-(65)=0

a = 4; b = 6; c = -65;
Δ = b2-4ac
Δ = 62-4·4·(-65)
Δ = 1076
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:

$\sqrt{\Delta}=\sqrt{1076}=\sqrt{4*269}=\sqrt{4}*\sqrt{269}=2\sqrt{269}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{269}}{2*4}=\frac{-6-2\sqrt{269}}{8}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{269}}{2*4}=\frac{-6+2\sqrt{269}}{8}
$