v2-20v=55

Solution for v2-20v=55 equation:

v2-20v=55

We move all terms to the left:

v2-20v-(55)=0

We add all the numbers together, and all the variables

v^2-20v-55=0

a = 1; b = -20; c = -55;
Δ = b2-4ac
Δ = -202-4·1·(-55)
Δ = 620
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:

$\sqrt{\Delta}=\sqrt{620}=\sqrt{4*155}=\sqrt{4}*\sqrt{155}=2\sqrt{155}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{155}}{2*1}=\frac{20-2\sqrt{155}}{2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{155}}{2*1}=\frac{20+2\sqrt{155}}{2}
$