-3v(v+4)=2v-37

Solution for -3v(v+4)=2v-37 equation:

-3v(v+4)=2v-37

We move all terms to the left:

-3v(v+4)-(2v-37)=0

We multiply parentheses

-3v^2-12v-(2v-37)=0

We get rid of parentheses

-3v^2-12v-2v+37=0

We add all the numbers together, and all the variables

-3v^2-14v+37=0

a = -3; b = -14; c = +37;
Δ = b2-4ac
Δ = -142-4·(-3)·37
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-8\sqrt{10}}{2*-3}=\frac{14-8\sqrt{10}}{-6}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+8\sqrt{10}}{2*-3}=\frac{14+8\sqrt{10}}{-6}
$