1/4y-y=-1

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

1/4y-y=-1

We move all terms to the left:

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -4; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·(-4)·1
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2}}{2*-4}=\frac{-4-4\sqrt{2}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2}}{2*-4}=\frac{-4+4\sqrt{2}}{-8}
$