1/2y=3.2y=20

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Solution for 1/2y=3.2y=20 equation:



1/2y=3.2y=20
We move all terms to the left:
1/2y-(3.2y)=0
Domain of the equation: 2y!=0
y!=0/2
y!=0
y∈R
We add all the numbers together, and all the variables
1/2y-(+3.2y)=0
We get rid of parentheses
1/2y-3.2y=0
We multiply all the terms by the denominator
-(3.2y)*2y+1=0
We add all the numbers together, and all the variables
-(+3.2y)*2y+1=0
We multiply parentheses
-6y^2+1=0
a = -6; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-6)·1
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*-6}=\frac{0-2\sqrt{6}}{-12} =-\frac{2\sqrt{6}}{-12} =-\frac{\sqrt{6}}{-6} $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*-6}=\frac{0+2\sqrt{6}}{-12} =\frac{2\sqrt{6}}{-12} =\frac{\sqrt{6}}{-6} $

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