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2y=5/2y-1
We move all terms to the left:
2y-(5/2y-1)=0
Domain of the equation: 2y-1)!=0We get rid of parentheses
y∈R
2y-5/2y+1=0
We multiply all the terms by the denominator
2y*2y+1*2y-5=0
Wy multiply elements
4y^2+2y-5=0
a = 4; b = 2; c = -5;
Δ = b2-4ac
Δ = 22-4·4·(-5)
Δ = 84
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{21}}{2*4}=\frac{-2-2\sqrt{21}}{8} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{21}}{2*4}=\frac{-2+2\sqrt{21}}{8} $
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