1/2y-(3-y)=5-2y

Solution for 1/2y-(3-y)=5-2y equation:

1/2y-(3-y)=5-2y

We move all terms to the left:

1/2y-(3-y)-(5-2y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

1/2y-(-1y+3)-(-2y+5)=0

We get rid of parentheses

1/2y+1y+2y-3-5=0

We multiply all the terms by the denominator


1y*2y+2y*2y-3*2y-5*2y+1=0

Wy multiply elements

2y^2+4y^2-6y-10y+1=0

We add all the numbers together, and all the variables

6y^2-16y+1=0

a = 6; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·6·1
Δ = 232
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:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{58}}{2*6}=\frac{16-2\sqrt{58}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{58}}{2*6}=\frac{16+2\sqrt{58}}{12}
$