389+506v=-3-147v^2-5v

Solution for 389+506v=-3-147v^2-5v equation:

389+506v=-3-147v^2-5v

We move all terms to the left:

389+506v-(-3-147v^2-5v)=0

We get rid of parentheses

147v^2+5v+506v+3+389=0

We add all the numbers together, and all the variables

147v^2+511v+392=0

a = 147; b = 511; c = +392;
Δ = b2-4ac
Δ = 5112-4·147·392
Δ = 30625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{30625}=175$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(511)-175}{2*147}=\frac{-686}{294}
=-2+1/3
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(511)+175}{2*147}=\frac{-336}{294}
=-1+1/7
$