81v^2-36v=4

Solution for 81v^2-36v=4 equation:

81v^2-36v=4

We move all terms to the left:

81v^2-36v-(4)=0

a = 81; b = -36; c = -4;
Δ = b2-4ac
Δ = -362-4·81·(-4)
Δ = 2592
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:

$\sqrt{\Delta}=\sqrt{2592}=\sqrt{1296*2}=\sqrt{1296}*\sqrt{2}=36\sqrt{2}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36\sqrt{2}}{2*81}=\frac{36-36\sqrt{2}}{162}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36\sqrt{2}}{2*81}=\frac{36+36\sqrt{2}}{162}
$