1/2*y=y-92

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

1/2y=y-92

We move all terms to the left:

1/2y-(y-92)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

1/2y-y+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}
$