3/2y+8=1/4y+2

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Solution for 3/2y+8=1/4y+2 equation:



3/2y+8=1/4y+2
We move all terms to the left:
3/2y+8-(1/4y+2)=0
Domain of the equation: 2y!=0
y!=0/2
y!=0
y∈R
Domain of the equation: 4y+2)!=0
y∈R
We get rid of parentheses
3/2y-1/4y-2+8=0
We calculate fractions
12y/8y^2+(-2y)/8y^2-2+8=0
We add all the numbers together, and all the variables
12y/8y^2+(-2y)/8y^2+6=0
We multiply all the terms by the denominator
12y+(-2y)+6*8y^2=0
Wy multiply elements
48y^2+12y+(-2y)=0
We get rid of parentheses
48y^2+12y-2y=0
We add all the numbers together, and all the variables
48y^2+10y=0
a = 48; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·48·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*48}=\frac{-20}{96} =-5/24 $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*48}=\frac{0}{96} =0 $

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