3/4y-6=1/y+10

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Solution for 3/4y-6=1/y+10 equation:



3/4y-6=1/y+10
We move all terms to the left:
3/4y-6-(1/y+10)=0
Domain of the equation: 4y!=0
y!=0/4
y!=0
y∈R
Domain of the equation: y+10)!=0
y∈R
We get rid of parentheses
3/4y-1/y-10-6=0
We calculate fractions
3y/4y^2+(-4y)/4y^2-10-6=0
We add all the numbers together, and all the variables
3y/4y^2+(-4y)/4y^2-16=0
We multiply all the terms by the denominator
3y+(-4y)-16*4y^2=0
Wy multiply elements
-64y^2+3y+(-4y)=0
We get rid of parentheses
-64y^2+3y-4y=0
We add all the numbers together, and all the variables
-64y^2-1y=0
a = -64; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-64)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-64}=\frac{0}{-128} =0 $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-64}=\frac{2}{-128} =-1/64 $

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