2v^2+36v+49=8v

Solution for 2v^2+36v+49=8v equation:

2v^2+36v+49=8v

We move all terms to the left:

2v^2+36v+49-(8v)=0

We add all the numbers together, and all the variables

2v^2+28v+49=0

a = 2; b = 28; c = +49;
Δ = b2-4ac
Δ = 282-4·2·49
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{-(28)-14\sqrt{2}}{2*2}=\frac{-28-14\sqrt{2}}{4}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+14\sqrt{2}}{2*2}=\frac{-28+14\sqrt{2}}{4}
$