(2/3)y-1=1/2

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

(2/3)y-1=1/2

We move all terms to the left:

(2/3)y-1-(1/2)=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

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

We multiply parentheses

2y^2-1-(+1/2)=0

We get rid of parentheses

2y^2-1-1/2=0

We multiply all the terms by the denominator


2y^2*2-1-1*2=0

We add all the numbers together, and all the variables

2y^2*2-3=0

Wy multiply elements

4y^2-3=0

a = 4; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·4·(-3)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*4}=\frac{0-4\sqrt{3}}{8}
=-\frac{4\sqrt{3}}{8}
=-\frac{\sqrt{3}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*4}=\frac{0+4\sqrt{3}}{8}
=\frac{4\sqrt{3}}{8}
=\frac{\sqrt{3}}{2}
$