2v^2=3v+119

Solution for 2v^2=3v+119 equation:

2v^2=3v+119

We move all terms to the left:

2v^2-(3v+119)=0

We get rid of parentheses

2v^2-3v-119=0

a = 2; b = -3; c = -119;
Δ = b2-4ac
Δ = -32-4·2·(-119)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-31}{2*2}=\frac{-28}{4}
=-7
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+31}{2*2}=\frac{34}{4}
=8+1/2
$