105v^2+182v=-56

Solution for 105v^2+182v=-56 equation:

105v^2+182v=-56

We move all terms to the left:

105v^2+182v-(-56)=0

We add all the numbers together, and all the variables

105v^2+182v+56=0

a = 105; b = 182; c = +56;
Δ = b2-4ac
Δ = 1822-4·105·56
Δ = 9604
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9604}=98$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(182)-98}{2*105}=\frac{-280}{210}
=-1+1/3
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(182)+98}{2*105}=\frac{-84}{210}
=-2/5
$