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3/8(-6-2y)=4/8(2y-3)

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Solution for 3/8(-6-2y)=4/8(2y-3) equation:



3/8(-6-2y)=4/8(2y-3)
We move all terms to the left:
3/8(-6-2y)-(4/8(2y-3))=0
Domain of the equation: 8(-6-2y)!=0
y∈R
Domain of the equation: 8(2y-3))!=0
y∈R
We add all the numbers together, and all the variables
3/8(-2y-6)-(4/8(2y-3))=0
We calculate fractions
(24y2/(8(-2y-6)*8(2y-3)))+(-32y0/(8(-2y-6)*8(2y-3)))=0
We calculate terms in parentheses: +(24y2/(8(-2y-6)*8(2y-3))), so:
24y2/(8(-2y-6)*8(2y-3))
We multiply all the terms by the denominator
24y2
We add all the numbers together, and all the variables
24y^2
Back to the equation:
+(24y^2)
We calculate terms in parentheses: +(-32y0/(8(-2y-6)*8(2y-3))), so:
-32y0/(8(-2y-6)*8(2y-3))
We multiply all the terms by the denominator
-32y0
We add all the numbers together, and all the variables
-32y
Back to the equation:
+(-32y)
We get rid of parentheses
24y^2-32y=0
a = 24; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·24·0
Δ = 1024
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{1024}=32
y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*24}=\frac{0}{48} =0
y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*24}=\frac{64}{48} =1+1/3

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