y-23(4)=1/2y

Solution for y-23(4)=1/2y equation:

y-23(4)=1/2y

We move all terms to the left:

y-23(4)-(1/2y)=0


Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

y-(+1/2y)-234=0

We get rid of parentheses

y-1/2y-234=0

We multiply all the terms by the denominator


y*2y-234*2y-1=0

Wy multiply elements

2y^2-468y-1=0

a = 2; b = -468; c = -1;
Δ = b2-4ac
Δ = -4682-4·2·(-1)
Δ = 219032
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:

$\sqrt{\Delta}=\sqrt{219032}=\sqrt{4*54758}=\sqrt{4}*\sqrt{54758}=2\sqrt{54758}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-468)-2\sqrt{54758}}{2*2}=\frac{468-2\sqrt{54758}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-468)+2\sqrt{54758}}{2*2}=\frac{468+2\sqrt{54758}}{4}
$