2v^2-4=7v

Solution for 2v^2-4=7v equation:

2v^2-4=7v

We move all terms to the left:

2v^2-4-(7v)=0

a = 2; b = -7; c = -4;
Δ = b2-4ac
Δ = -72-4·2·(-4)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-9}{2*2}=\frac{-2}{4}
=-1/2
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+9}{2*2}=\frac{16}{4}
=4
$