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y-5/6y=19
We move all terms to the left:
y-5/6y-(19)=0
Domain of the equation: 6y!=0We multiply all the terms by the denominator
y!=0/6
y!=0
y∈R
y*6y-19*6y-5=0
Wy multiply elements
6y^2-114y-5=0
a = 6; b = -114; c = -5;
Δ = b2-4ac
Δ = -1142-4·6·(-5)
Δ = 13116
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{13116}=\sqrt{4*3279}=\sqrt{4}*\sqrt{3279}=2\sqrt{3279}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-2\sqrt{3279}}{2*6}=\frac{114-2\sqrt{3279}}{12} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+2\sqrt{3279}}{2*6}=\frac{114+2\sqrt{3279}}{12} $
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