1/2y=3.2y=20

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}
$