10(v+1)-4v=3(*2v+4)-13

Solution for 10(v+1)-4v=3(*2v+4)-13 equation:

10(v+1)-4v=3(*2v+4)-13

We move all terms to the left:

10(v+1)-4v-(3(*2v+4)-13)=0

We add all the numbers together, and all the variables

-4v+10(v+1)-(3(*2v+4)-13)=0

We multiply parentheses

-4v+10v-(3(*2v+4)-13)+10=0


We calculate terms in parentheses: -(3(*2v+4)-13), so:

3(*2v+4)-13

We multiply parentheses

6v^2+12-13

We add all the numbers together, and all the variables

6v^2-1

Back to the equation:

-(6v^2-1)


We add all the numbers together, and all the variables

6v-(6v^2-1)+10=0

We get rid of parentheses

-6v^2+6v+1+10=0

We add all the numbers together, and all the variables

-6v^2+6v+11=0

a = -6; b = 6; c = +11;
Δ = b2-4ac
Δ = 62-4·(-6)·11
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-10\sqrt{3}}{2*-6}=\frac{-6-10\sqrt{3}}{-12}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+10\sqrt{3}}{2*-6}=\frac{-6+10\sqrt{3}}{-12}
$