6v(v-4)-1=-3(-8v+7)-2v

Solution for 6v(v-4)-1=-3(-8v+7)-2v equation:

6v(v-4)-1=-3(-8v+7)-2v

We move all terms to the left:

6v(v-4)-1-(-3(-8v+7)-2v)=0

We multiply parentheses

6v^2-24v-(-3(-8v+7)-2v)-1=0


We calculate terms in parentheses: -(-3(-8v+7)-2v), so:

-3(-8v+7)-2v

We add all the numbers together, and all the variables

-2v-3(-8v+7)

We multiply parentheses

-2v+24v-21

We add all the numbers together, and all the variables

22v-21

Back to the equation:

-(22v-21)


We get rid of parentheses

6v^2-24v-22v+21-1=0

We add all the numbers together, and all the variables

6v^2-46v+20=0

a = 6; b = -46; c = +20;
Δ = b2-4ac
Δ = -462-4·6·20
Δ = 1636
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:

$\sqrt{\Delta}=\sqrt{1636}=\sqrt{4*409}=\sqrt{4}*\sqrt{409}=2\sqrt{409}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{409}}{2*6}=\frac{46-2\sqrt{409}}{12}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{409}}{2*6}=\frac{46+2\sqrt{409}}{12}
$