84=7v^2+28

Solution for 84=7v^2+28 equation:

84=7v^2+28

We move all terms to the left:

84-(7v^2+28)=0

We get rid of parentheses

-7v^2-28+84=0

We add all the numbers together, and all the variables

-7v^2+56=0

a = -7; b = 0; c = +56;
Δ = b2-4ac
Δ = 02-4·(-7)·56
Δ = 1568
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:

$\sqrt{\Delta}=\sqrt{1568}=\sqrt{784*2}=\sqrt{784}*\sqrt{2}=28\sqrt{2}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{2}}{2*-7}=\frac{0-28\sqrt{2}}{-14}
=-\frac{28\sqrt{2}}{-14}
=-\frac{2\sqrt{2}}{-1}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{2}}{2*-7}=\frac{0+28\sqrt{2}}{-14}
=\frac{28\sqrt{2}}{-14}
=\frac{2\sqrt{2}}{-1}
$