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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

5v-18v-(2v(v+6))+9=0


We calculate terms in parentheses: -(2v(v+6)), so:

2v(v+6)

We multiply parentheses

2v^2+12v

Back to the equation:

-(2v^2+12v)


We add all the numbers together, and all the variables

-13v-(2v^2+12v)+9=0

We get rid of parentheses

-2v^2-13v-12v+9=0

We add all the numbers together, and all the variables

-2v^2-25v+9=0

a = -2; b = -25; c = +9;
Δ = b2-4ac
Δ = -252-4·(-2)·9
Δ = 697
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-\sqrt{697}}{2*-2}=\frac{25-\sqrt{697}}{-4}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{697}}{2*-2}=\frac{25+\sqrt{697}}{-4}
$