y-92=1/2y

Solution for y-92=1/2y equation:

y-92=1/2y

We move all terms to the left:

y-92-(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)-92=0

We get rid of parentheses

y-1/2y-92=0

We multiply all the terms by the denominator


y*2y-92*2y-1=0

Wy multiply elements

2y^2-184y-1=0

a = 2; b = -184; c = -1;
Δ = b2-4ac
Δ = -1842-4·2·(-1)
Δ = 33864
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:

$\sqrt{\Delta}=\sqrt{33864}=\sqrt{4*8466}=\sqrt{4}*\sqrt{8466}=2\sqrt{8466}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-184)-2\sqrt{8466}}{2*2}=\frac{184-2\sqrt{8466}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-184)+2\sqrt{8466}}{2*2}=\frac{184+2\sqrt{8466}}{4}
$