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2/3(y)=y-62
We move all terms to the left:
2/3(y)-(y-62)=0
Domain of the equation: 3y!=0We get rid of parentheses
y!=0/3
y!=0
y∈R
2/3y-y+62=0
We multiply all the terms by the denominator
-y*3y+62*3y+2=0
Wy multiply elements
-3y^2+186y+2=0
a = -3; b = 186; c = +2;
Δ = b2-4ac
Δ = 1862-4·(-3)·2
Δ = 34620
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{34620}=\sqrt{4*8655}=\sqrt{4}*\sqrt{8655}=2\sqrt{8655}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(186)-2\sqrt{8655}}{2*-3}=\frac{-186-2\sqrt{8655}}{-6} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(186)+2\sqrt{8655}}{2*-3}=\frac{-186+2\sqrt{8655}}{-6} $
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