v^2-2v-97=0

Solution for v^2-2v-97=0 equation:

v^2-2v-97=0

a = 1; b = -2; c = -97;
Δ = b2-4ac
Δ = -22-4·1·(-97)
Δ = 392
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-14\sqrt{2}}{2*1}=\frac{2-14\sqrt{2}}{2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14\sqrt{2}}{2*1}=\frac{2+14\sqrt{2}}{2}
$