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105/y=8+y
We move all terms to the left:
105/y-(8+y)=0
Domain of the equation: y!=0We add all the numbers together, and all the variables
y∈R
105/y-(y+8)=0
We get rid of parentheses
105/y-y-8=0
We multiply all the terms by the denominator
-y*y-8*y+105=0
We add all the numbers together, and all the variables
-8y-y*y+105=0
Wy multiply elements
-1y^2-8y+105=0
a = -1; b = -8; c = +105;
Δ = b2-4ac
Δ = -82-4·(-1)·105
Δ = 484
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{484}=22$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-22}{2*-1}=\frac{-14}{-2} =+7 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+22}{2*-1}=\frac{30}{-2} =-15 $
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