7v^2+4=-17v

Solution for 7v^2+4=-17v equation:

7v^2+4=-17v

We move all terms to the left:

7v^2+4-(-17v)=0

We get rid of parentheses

7v^2+17v+4=0

a = 7; b = 17; c = +4;
Δ = b2-4ac
Δ = 172-4·7·4
Δ = 177
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{-(17)-\sqrt{177}}{2*7}=\frac{-17-\sqrt{177}}{14}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{177}}{2*7}=\frac{-17+\sqrt{177}}{14}
$