-4(v+4)2v+5=7v+7

Solution for -4(v+4)2v+5=7v+7 equation:

-4(v+4)2v+5=7v+7

We move all terms to the left:

-4(v+4)2v+5-(7v+7)=0

We multiply parentheses

-8v^2-32v-(7v+7)+5=0

We get rid of parentheses

-8v^2-32v-7v-7+5=0

We add all the numbers together, and all the variables

-8v^2-39v-2=0

a = -8; b = -39; c = -2;
Δ = b2-4ac
Δ = -392-4·(-8)·(-2)
Δ = 1457
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{-(-39)-\sqrt{1457}}{2*-8}=\frac{39-\sqrt{1457}}{-16}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1457}}{2*-8}=\frac{39+\sqrt{1457}}{-16}
$