1/4y+8=-4y-1

Solution for 1/4y+8=-4y-1 equation:

1/4y+8=-4y-1

We move all terms to the left:

1/4y+8-(-4y-1)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We get rid of parentheses

1/4y+4y+1+8=0

We multiply all the terms by the denominator


4y*4y+1*4y+8*4y+1=0

Wy multiply elements

16y^2+4y+32y+1=0

We add all the numbers together, and all the variables

16y^2+36y+1=0

a = 16; b = 36; c = +1;
Δ = b2-4ac
Δ = 362-4·16·1
Δ = 1232
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:

$\sqrt{\Delta}=\sqrt{1232}=\sqrt{16*77}=\sqrt{16}*\sqrt{77}=4\sqrt{77}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{77}}{2*16}=\frac{-36-4\sqrt{77}}{32}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{77}}{2*16}=\frac{-36+4\sqrt{77}}{32}
$