-5v^2-v+12=6v

Solution for -5v^2-v+12=6v equation:

-5v^2-v+12=6v

We move all terms to the left:

-5v^2-v+12-(6v)=0

We add all the numbers together, and all the variables

-5v^2-7v+12=0

a = -5; b = -7; c = +12;
Δ = b2-4ac
Δ = -72-4·(-5)·12
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-17}{2*-5}=\frac{-10}{-10}
=1
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+17}{2*-5}=\frac{24}{-10}
=-2+2/5
$