y=-1/2y+8

Solution for y=-1/2y+8 equation:

y=-1/2y+8

We move all terms to the left:

y-(-1/2y+8)=0


Domain of the equation: 2y+8)!=0

y∈R


We get rid of parentheses

y+1/2y-8=0

We multiply all the terms by the denominator


y*2y-8*2y+1=0

Wy multiply elements

2y^2-16y+1=0

a = 2; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·2·1
Δ = 248
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:

$\sqrt{\Delta}=\sqrt{248}=\sqrt{4*62}=\sqrt{4}*\sqrt{62}=2\sqrt{62}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{62}}{2*2}=\frac{16-2\sqrt{62}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{62}}{2*2}=\frac{16+2\sqrt{62}}{4}
$