-y+1/4y=9

Solution for -y+1/4y=9 equation:

-y+1/4y=9

We move all terms to the left:

-y+1/4y-(9)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

-1y+1/4y-9=0

We multiply all the terms by the denominator


-1y*4y-9*4y+1=0

Wy multiply elements

-4y^2-36y+1=0

a = -4; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·(-4)·1
Δ = 1312
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:

$\sqrt{\Delta}=\sqrt{1312}=\sqrt{16*82}=\sqrt{16}*\sqrt{82}=4\sqrt{82}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{82}}{2*-4}=\frac{36-4\sqrt{82}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{82}}{2*-4}=\frac{36+4\sqrt{82}}{-8}
$