-2(5v-7)6v=5+3(2v-2)

Solution for -2(5v-7)6v=5+3(2v-2) equation:

-2(5v-7)6v=5+3(2v-2)

We move all terms to the left:

-2(5v-7)6v-(5+3(2v-2))=0

We multiply parentheses

-60v^2+84v-(5+3(2v-2))=0


We calculate terms in parentheses: -(5+3(2v-2)), so:

5+3(2v-2)

determiningTheFunctionDomain
3(2v-2)+5

We multiply parentheses

6v-6+5

We add all the numbers together, and all the variables

6v-1

Back to the equation:

-(6v-1)


We get rid of parentheses

-60v^2+84v-6v+1=0

We add all the numbers together, and all the variables

-60v^2+78v+1=0

a = -60; b = 78; c = +1;
Δ = b2-4ac
Δ = 782-4·(-60)·1
Δ = 6324
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:

$\sqrt{\Delta}=\sqrt{6324}=\sqrt{4*1581}=\sqrt{4}*\sqrt{1581}=2\sqrt{1581}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-2\sqrt{1581}}{2*-60}=\frac{-78-2\sqrt{1581}}{-120}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+2\sqrt{1581}}{2*-60}=\frac{-78+2\sqrt{1581}}{-120}
$