8v^2+5-6v^2=61

Solution for 8v^2+5-6v^2=61 equation:

8v^2+5-6v^2=61

We move all terms to the left:

8v^2+5-6v^2-(61)=0

We add all the numbers together, and all the variables

2v^2-56=0

a = 2; b = 0; c = -56;
Δ = b2-4ac
Δ = 02-4·2·(-56)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{7}}{2*2}=\frac{0-8\sqrt{7}}{4}
=-\frac{8\sqrt{7}}{4}
=-2\sqrt{7}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{7}}{2*2}=\frac{0+8\sqrt{7}}{4}
=\frac{8\sqrt{7}}{4}
=2\sqrt{7}
$