-4(v+3)=-14(v2-4v)

Solution for -4(v+3)=-14(v2-4v) equation:

-4(v+3)=-14(v2-4v)

We move all terms to the left:

-4(v+3)-(-14(v2-4v))=0

We add all the numbers together, and all the variables

-(-14(+v^2-4v))-4(v+3)=0

We multiply parentheses

-(-14(+v^2-4v))-4v-12=0


We calculate terms in parentheses: -(-14(+v^2-4v)), so:

-14(+v^2-4v)

We multiply parentheses

-14v^2+56v

Back to the equation:

-(-14v^2+56v)


We get rid of parentheses

14v^2-56v-4v-12=0

We add all the numbers together, and all the variables

14v^2-60v-12=0

a = 14; b = -60; c = -12;
Δ = b2-4ac
Δ = -602-4·14·(-12)
Δ = 4272
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:

$\sqrt{\Delta}=\sqrt{4272}=\sqrt{16*267}=\sqrt{16}*\sqrt{267}=4\sqrt{267}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{267}}{2*14}=\frac{60-4\sqrt{267}}{28}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{267}}{2*14}=\frac{60+4\sqrt{267}}{28}
$