7v^2-14v-5=3

Solution for 7v^2-14v-5=3 equation:

7v^2-14v-5=3

We move all terms to the left:

7v^2-14v-5-(3)=0

We add all the numbers together, and all the variables

7v^2-14v-8=0

a = 7; b = -14; c = -8;
Δ = b2-4ac
Δ = -142-4·7·(-8)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{105}}{2*7}=\frac{14-2\sqrt{105}}{14}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{105}}{2*7}=\frac{14+2\sqrt{105}}{14}
$