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1/4y+8=-4y-1
We move all terms to the left:
1/4y+8-(-4y-1)=0
Domain of the equation: 4y!=0We get rid of parentheses
y!=0/4
y!=0
y∈R
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} $
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