6v^2=-42v

Solution for 6v^2=-42v equation:

6v^2=-42v

We move all terms to the left:

6v^2-(-42v)=0

We get rid of parentheses

6v^2+42v=0

a = 6; b = 42; c = 0;
Δ = b2-4ac
Δ = 422-4·6·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-42}{2*6}=\frac{-84}{12}
=-7
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+42}{2*6}=\frac{0}{12}
=0
$