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4y-7/2y=9
We move all terms to the left:
4y-7/2y-(9)=0
Domain of the equation: 2y!=0We multiply all the terms by the denominator
y!=0/2
y!=0
y∈R
4y*2y-9*2y-7=0
Wy multiply elements
8y^2-18y-7=0
a = 8; b = -18; c = -7;
Δ = b2-4ac
Δ = -182-4·8·(-7)
Δ = 548
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{548}=\sqrt{4*137}=\sqrt{4}*\sqrt{137}=2\sqrt{137}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{137}}{2*8}=\frac{18-2\sqrt{137}}{16} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{137}}{2*8}=\frac{18+2\sqrt{137}}{16} $
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