2/3(18y)=y

Solution for 2/3(18y)=y equation:

2/3(18y)=y

We move all terms to the left:

2/3(18y)-(y)=0


Domain of the equation: 318y!=0

y!=0/318

y!=0

y∈R


We add all the numbers together, and all the variables

-1y+2/318y=0

We multiply all the terms by the denominator


-1y*318y+2=0

Wy multiply elements

-318y^2+2=0

a = -318; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-318)·2
Δ = 2544
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:

$\sqrt{\Delta}=\sqrt{2544}=\sqrt{16*159}=\sqrt{16}*\sqrt{159}=4\sqrt{159}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{159}}{2*-318}=\frac{0-4\sqrt{159}}{-636}
=-\frac{4\sqrt{159}}{-636}
=-\frac{\sqrt{159}}{-159}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{159}}{2*-318}=\frac{0+4\sqrt{159}}{-636}
=\frac{4\sqrt{159}}{-636}
=\frac{\sqrt{159}}{-159}
$