3/5v=10;v=25

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Solution for 3/5v=10;v=25 equation:



3/5v=10v=25
We move all terms to the left:
3/5v-(10v)=0
Domain of the equation: 5v!=0
v!=0/5
v!=0
v∈R
We add all the numbers together, and all the variables
-10v+3/5v=0
We multiply all the terms by the denominator
-10v*5v+3=0
Wy multiply elements
-50v^2+3=0
a = -50; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-50)·3
Δ = 600
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:
$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*-50}=\frac{0-10\sqrt{6}}{-100} =-\frac{10\sqrt{6}}{-100} =-\frac{\sqrt{6}}{-10} $
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*-50}=\frac{0+10\sqrt{6}}{-100} =\frac{10\sqrt{6}}{-100} =\frac{\sqrt{6}}{-10} $

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