4v2+4=-17v

Solution for 4v2+4=-17v equation:

4v^2+4=-17v

We move all terms to the left:

4v^2+4-(-17v)=0

We get rid of parentheses

4v^2+17v+4=0

a = 4; b = 17; c = +4;
Δ = b2-4ac
Δ = 172-4·4·4
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-15}{2*4}=\frac{-32}{8}
=-4
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+15}{2*4}=\frac{-2}{8}
=-1/4
$