2/3y=44y=

Solution for 2/3y=44y= equation:

2/3y=44y=

We move all terms to the left:

2/3y-(44y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

-44y+2/3y=0

We multiply all the terms by the denominator


-44y*3y+2=0

Wy multiply elements

-132y^2+2=0

a = -132; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-132)·2
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{66}}{2*-132}=\frac{0-4\sqrt{66}}{-264}
=-\frac{4\sqrt{66}}{-264}
=-\frac{\sqrt{66}}{-66}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{66}}{2*-132}=\frac{0+4\sqrt{66}}{-264}
=\frac{4\sqrt{66}}{-264}
=\frac{\sqrt{66}}{-66}
$