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 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 = 33848
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:

$\sqrt{\Delta}=\sqrt{33848}=\sqrt{4*8462}=\sqrt{4}*\sqrt{8462}=2\sqrt{8462}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-184)-2\sqrt{8462}}{2*2}=\frac{184-2\sqrt{8462}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-184)+2\sqrt{8462}}{2*2}=\frac{184+2\sqrt{8462}}{4}
$