3(v+2)7v=-18

Solution for 3(v+2)7v=-18 equation:

3(v+2)7v=-18

We move all terms to the left:

3(v+2)7v-(-18)=0

We add all the numbers together, and all the variables

3(v+2)7v+18=0

We multiply parentheses

21v^2+42v+18=0

a = 21; b = 42; c = +18;
Δ = b2-4ac
Δ = 422-4·21·18
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{7}}{2*21}=\frac{-42-6\sqrt{7}}{42}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{7}}{2*21}=\frac{-42+6\sqrt{7}}{42}
$