5v^2-27v+4=-6

Solution for 5v^2-27v+4=-6 equation:

5v^2-27v+4=-6

We move all terms to the left:

5v^2-27v+4-(-6)=0

We add all the numbers together, and all the variables

5v^2-27v+10=0

a = 5; b = -27; c = +10;
Δ = b2-4ac
Δ = -272-4·5·10
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-23}{2*5}=\frac{4}{10}
=2/5
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+23}{2*5}=\frac{50}{10}
=5
$