2(v-6)-9=-3(-8v+8)7v

Solution for 2(v-6)-9=-3(-8v+8)7v equation:

2(v-6)-9=-3(-8v+8)7v

We move all terms to the left:

2(v-6)-9-(-3(-8v+8)7v)=0

We multiply parentheses

2v-(-3(-8v+8)7v)-12-9=0


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

-3(-8v+8)7v

We multiply parentheses

168v^2-168v

Back to the equation:

-(168v^2-168v)


We add all the numbers together, and all the variables

2v-(168v^2-168v)-21=0

We get rid of parentheses

-168v^2+2v+168v-21=0

We add all the numbers together, and all the variables

-168v^2+170v-21=0

a = -168; b = 170; c = -21;
Δ = b2-4ac
Δ = 1702-4·(-168)·(-21)
Δ = 14788
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:

$\sqrt{\Delta}=\sqrt{14788}=\sqrt{4*3697}=\sqrt{4}*\sqrt{3697}=2\sqrt{3697}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(170)-2\sqrt{3697}}{2*-168}=\frac{-170-2\sqrt{3697}}{-336}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(170)+2\sqrt{3697}}{2*-168}=\frac{-170+2\sqrt{3697}}{-336}
$