y-1/2y=7

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Solution for y-1/2y=7 equation:



y-1/2y=7
We move all terms to the left:
y-1/2y-(7)=0
Domain of the equation: 2y!=0
y!=0/2
y!=0
y∈R
We multiply all the terms by the denominator
y*2y-7*2y-1=0
Wy multiply elements
2y^2-14y-1=0
a = 2; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·2·(-1)
Δ = 204
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:
$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{51}}{2*2}=\frac{14-2\sqrt{51}}{4} $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{51}}{2*2}=\frac{14+2\sqrt{51}}{4} $

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