y=10-1/4y

Solution for y=10-1/4y equation:

y=10-1/4y

We move all terms to the left:

y-(10-1/4y)=0


Domain of the equation: 4y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

y-(-1/4y+10)=0

We get rid of parentheses

y+1/4y-10=0

We multiply all the terms by the denominator


y*4y-10*4y+1=0

Wy multiply elements

4y^2-40y+1=0

a = 4; b = -40; c = +1;
Δ = b2-4ac
Δ = -402-4·4·1
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-12\sqrt{11}}{2*4}=\frac{40-12\sqrt{11}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+12\sqrt{11}}{2*4}=\frac{40+12\sqrt{11}}{8}
$