6(v-3)v-3=5

Solution for 6(v-3)v-3=5 equation:

6(v-3)v-3=5

We move all terms to the left:

6(v-3)v-3-(5)=0

We add all the numbers together, and all the variables

6(v-3)v-8=0

We multiply parentheses

6v^2-18v-8=0

a = 6; b = -18; c = -8;
Δ = b2-4ac
Δ = -182-4·6·(-8)
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{129}}{2*6}=\frac{18-2\sqrt{129}}{12}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{129}}{2*6}=\frac{18+2\sqrt{129}}{12}
$