1v(780*6+4v*12)=372

Solution for 1v(780*6+4v*12)=372 equation:

1v(780*6+4v*12)=372

We move all terms to the left:

1v(780*6+4v*12)-(372)=0

We add all the numbers together, and all the variables

1v(4v*12+4680)-372=0

We multiply parentheses

48v^2+4680v-372=0

a = 48; b = 4680; c = -372;
Δ = b2-4ac
Δ = 46802-4·48·(-372)
Δ = 21973824
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:

$\sqrt{\Delta}=\sqrt{21973824}=\sqrt{576*38149}=\sqrt{576}*\sqrt{38149}=24\sqrt{38149}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4680)-24\sqrt{38149}}{2*48}=\frac{-4680-24\sqrt{38149}}{96}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4680)+24\sqrt{38149}}{2*48}=\frac{-4680+24\sqrt{38149}}{96}
$