y=28-21/2y

Solution for y=28-21/2y equation:

y=28-21/2y

We move all terms to the left:

y-(28-21/2y)=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-(-21/2y+28)=0

We get rid of parentheses

y+21/2y-28=0

We multiply all the terms by the denominator


y*2y-28*2y+21=0

Wy multiply elements

2y^2-56y+21=0

a = 2; b = -56; c = +21;
Δ = b2-4ac
Δ = -562-4·2·21
Δ = 2968
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:

$\sqrt{\Delta}=\sqrt{2968}=\sqrt{4*742}=\sqrt{4}*\sqrt{742}=2\sqrt{742}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-2\sqrt{742}}{2*2}=\frac{56-2\sqrt{742}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+2\sqrt{742}}{2*2}=\frac{56+2\sqrt{742}}{4}
$