(1/3*y)-18=2

Solution for (1/3*y)-18=2 equation:

(1/3*y)-18=2

We move all terms to the left:

(1/3*y)-18-(2)=0


Domain of the equation: 3*y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+1/3*y)-18-2=0

We add all the numbers together, and all the variables

(+1/3*y)-20=0

We get rid of parentheses

1/3*y-20=0

We multiply all the terms by the denominator


-20*3*y+1=0

Wy multiply elements

-60y*y+1=0

Wy multiply elements

-60y^2+1=0

a = -60; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-60)·1
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*-60}=\frac{0-4\sqrt{15}}{-120}
=-\frac{4\sqrt{15}}{-120}
=-\frac{\sqrt{15}}{-30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*-60}=\frac{0+4\sqrt{15}}{-120}
=\frac{4\sqrt{15}}{-120}
=\frac{\sqrt{15}}{-30}
$