40v=-37v^2

Solution for 40v=-37v^2 equation:

40v=-37v^2

We move all terms to the left:

40v-(-37v^2)=0

We get rid of parentheses

37v^2+40v=0

a = 37; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·37·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*37}=\frac{-80}{74}
=-1+3/37
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*37}=\frac{0}{74}
=0
$