6-6v^2=-109

Solution for 6-6v^2=-109 equation:

6-6v^2=-109

We move all terms to the left:

6-6v^2-(-109)=0

We add all the numbers together, and all the variables

-6v^2+115=0

a = -6; b = 0; c = +115;
Δ = b2-4ac
Δ = 02-4·(-6)·115
Δ = 2760
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:

$\sqrt{\Delta}=\sqrt{2760}=\sqrt{4*690}=\sqrt{4}*\sqrt{690}=2\sqrt{690}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{690}}{2*-6}=\frac{0-2\sqrt{690}}{-12}
=-\frac{2\sqrt{690}}{-12}
=-\frac{\sqrt{690}}{-6}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{690}}{2*-6}=\frac{0+2\sqrt{690}}{-12}
=\frac{2\sqrt{690}}{-12}
=\frac{\sqrt{690}}{-6}
$