23.75-(1/4)y=y

Solution for 23.75-(1/4)y=y equation:

23.75-(1/4)y=y

We move all terms to the left:

23.75-(1/4)y-(y)=0


Domain of the equation: 4)y!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

-(+1/4)y-y+23.75=0

We add all the numbers together, and all the variables

-1y-(+1/4)y+23.75=0

We multiply parentheses

-y^2-1y+23.75=0

We add all the numbers together, and all the variables

-1y^2-1y+23.75=0

a = -1; b = -1; c = +23.75;
Δ = b2-4ac
Δ = -12-4·(-1)·23.75
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-4\sqrt{6}}{2*-1}=\frac{1-4\sqrt{6}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+4\sqrt{6}}{2*-1}=\frac{1+4\sqrt{6}}{-2}
$