3/2y=55y

Solution for 3/2y=55y equation:

3/2y=55y

We move all terms to the left:

3/2y-(55y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

-55y+3/2y=0

We multiply all the terms by the denominator


-55y*2y+3=0

Wy multiply elements

-110y^2+3=0

a = -110; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-110)·3
Δ = 1320
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:

$\sqrt{\Delta}=\sqrt{1320}=\sqrt{4*330}=\sqrt{4}*\sqrt{330}=2\sqrt{330}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{330}}{2*-110}=\frac{0-2\sqrt{330}}{-220}
=-\frac{2\sqrt{330}}{-220}
=-\frac{\sqrt{330}}{-110}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{330}}{2*-110}=\frac{0+2\sqrt{330}}{-220}
=\frac{2\sqrt{330}}{-220}
=\frac{\sqrt{330}}{-110}
$