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(35y-20)/(18y+99)=y
We move all terms to the left:
(35y-20)/(18y+99)-(y)=0
Domain of the equation: (18y+99)!=0We add all the numbers together, and all the variables
We move all terms containing y to the left, all other terms to the right
18y!=-99
y!=-99/18
y!=-5+1/2
y∈R
-1y+(35y-20)/(18y+99)=0
We multiply all the terms by the denominator
-1y*(18y+99)+(35y-20)=0
We multiply parentheses
-18y^2-99y+(35y-20)=0
We get rid of parentheses
-18y^2-99y+35y-20=0
We add all the numbers together, and all the variables
-18y^2-64y-20=0
a = -18; b = -64; c = -20;
Δ = b2-4ac
Δ = -642-4·(-18)·(-20)
Δ = 2656
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2656}=\sqrt{16*166}=\sqrt{16}*\sqrt{166}=4\sqrt{166}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-4\sqrt{166}}{2*-18}=\frac{64-4\sqrt{166}}{-36} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+4\sqrt{166}}{2*-18}=\frac{64+4\sqrt{166}}{-36} $
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