65=v2/5+19

Solution for 65=v2/5+19 equation:

65=v2/5+19

We move all terms to the left:

65-(v2/5+19)=0

We get rid of parentheses

-v2/5-19+65=0

We multiply all the terms by the denominator


-v2-19*5+65*5=0

We add all the numbers together, and all the variables

-1v^2+230=0

a = -1; b = 0; c = +230;
Δ = b2-4ac
Δ = 02-4·(-1)·230
Δ = 920
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:

$\sqrt{\Delta}=\sqrt{920}=\sqrt{4*230}=\sqrt{4}*\sqrt{230}=2\sqrt{230}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{230}}{2*-1}=\frac{0-2\sqrt{230}}{-2}
=-\frac{2\sqrt{230}}{-2}
=-\frac{\sqrt{230}}{-1}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{230}}{2*-1}=\frac{0+2\sqrt{230}}{-2}
=\frac{2\sqrt{230}}{-2}
=\frac{\sqrt{230}}{-1}
$