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/6Y=8+2Y
We move all terms to the left:
/6Y-(8+2Y)=0
Domain of the equation: 6Y!=0We add all the numbers together, and all the variables
Y!=0/6
Y!=0
Y∈R
/6Y-(2Y+8)=0
We get rid of parentheses
/6Y-2Y-8=0
We multiply all the terms by the denominator
-2Y*6Y-8*6Y+=0
We add all the numbers together, and all the variables
-2Y*6Y-8*6Y=0
Wy multiply elements
-12Y^2-48Y=0
a = -12; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·(-12)·0
Δ = 2304
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{2304}=48$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48}{2*-12}=\frac{0}{-24} =0 $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*-12}=\frac{96}{-24} =-4 $
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