1/2y=y-23

Solution for 1/2y=y-23 equation:

1/2y=y-23

We move all terms to the left:

1/2y-(y-23)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

1/2y-y+23=0

We multiply all the terms by the denominator


-y*2y+23*2y+1=0

Wy multiply elements

-2y^2+46y+1=0

a = -2; b = 46; c = +1;
Δ = b2-4ac
Δ = 462-4·(-2)·1
Δ = 2124
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:

$\sqrt{\Delta}=\sqrt{2124}=\sqrt{36*59}=\sqrt{36}*\sqrt{59}=6\sqrt{59}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-6\sqrt{59}}{2*-2}=\frac{-46-6\sqrt{59}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+6\sqrt{59}}{2*-2}=\frac{-46+6\sqrt{59}}{-4}
$