-3v(v-1)=7v-37

Solution for -3v(v-1)=7v-37 equation:

-3v(v-1)=7v-37

We move all terms to the left:

-3v(v-1)-(7v-37)=0

We multiply parentheses

-3v^2+3v-(7v-37)=0

We get rid of parentheses

-3v^2+3v-7v+37=0

We add all the numbers together, and all the variables

-3v^2-4v+37=0

a = -3; b = -4; c = +37;
Δ = b2-4ac
Δ = -42-4·(-3)·37
Δ = 460
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:

$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{115}}{2*-3}=\frac{4-2\sqrt{115}}{-6}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{115}}{2*-3}=\frac{4+2\sqrt{115}}{-6}
$