-38+4v=-3v(v+1)-7

Solution for -38+4v=-3v(v+1)-7 equation:

-38+4v=-3v(v+1)-7

We move all terms to the left:

-38+4v-(-3v(v+1)-7)=0


We calculate terms in parentheses: -(-3v(v+1)-7), so:

-3v(v+1)-7

We multiply parentheses

-3v^2-3v-7

Back to the equation:

-(-3v^2-3v-7)


We get rid of parentheses

3v^2+3v+4v+7-38=0

We add all the numbers together, and all the variables

3v^2+7v-31=0

a = 3; b = 7; c = -31;
Δ = b2-4ac
Δ = 72-4·3·(-31)
Δ = 421
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{-(7)-\sqrt{421}}{2*3}=\frac{-7-\sqrt{421}}{6}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{421}}{2*3}=\frac{-7+\sqrt{421}}{6}
$