v^2=-9v+17

Solution for v^2=-9v+17 equation:

v^2=-9v+17

We move all terms to the left:

v^2-(-9v+17)=0

We get rid of parentheses

v^2+9v-17=0

a = 1; b = 9; c = -17;
Δ = b2-4ac
Δ = 92-4·1·(-17)
Δ = 149
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{-(9)-\sqrt{149}}{2*1}=\frac{-9-\sqrt{149}}{2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{149}}{2*1}=\frac{-9+\sqrt{149}}{2}
$