48=v2

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Solution for 48=v2 equation:



48=v2
We move all terms to the left:
48-(v2)=0
We add all the numbers together, and all the variables
-1v^2+48=0
a = -1; b = 0; c = +48;
Δ = b2-4ac
Δ = 02-4·(-1)·48
Δ = 192
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:
$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*-1}=\frac{0-8\sqrt{3}}{-2} =-\frac{8\sqrt{3}}{-2} =-\frac{4\sqrt{3}}{-1} $
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*-1}=\frac{0+8\sqrt{3}}{-2} =\frac{8\sqrt{3}}{-2} =\frac{4\sqrt{3}}{-1} $

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