3v^2=36v+49=8v

Solution for 3v^2=36v+49=8v equation:

3v^2=36v+49=8v

We move all terms to the left:

3v^2-(36v+49)=0

We get rid of parentheses

3v^2-36v-49=0

a = 3; b = -36; c = -49;
Δ = b2-4ac
Δ = -362-4·3·(-49)
Δ = 1884
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:

$\sqrt{\Delta}=\sqrt{1884}=\sqrt{4*471}=\sqrt{4}*\sqrt{471}=2\sqrt{471}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{471}}{2*3}=\frac{36-2\sqrt{471}}{6}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{471}}{2*3}=\frac{36+2\sqrt{471}}{6}
$