v^2-18v=19

Solution for v^2-18v=19 equation:

v^2-18v=19

We move all terms to the left:

v^2-18v-(19)=0

a = 1; b = -18; c = -19;
Δ = b2-4ac
Δ = -182-4·1·(-19)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-20}{2*1}=\frac{-2}{2}
=-1
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+20}{2*1}=\frac{38}{2}
=19
$