2v^2+10v+7=4

Solution for 2v^2+10v+7=4 equation:

2v^2+10v+7=4

We move all terms to the left:

2v^2+10v+7-(4)=0

We add all the numbers together, and all the variables

2v^2+10v+3=0

a = 2; b = 10; c = +3;
Δ = b2-4ac
Δ = 102-4·2·3
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{19}}{2*2}=\frac{-10-2\sqrt{19}}{4}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{19}}{2*2}=\frac{-10+2\sqrt{19}}{4}
$