5y-7/2y=3

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Solution for 5y-7/2y=3 equation:



5y-7/2y=3
We move all terms to the left:
5y-7/2y-(3)=0
Domain of the equation: 2y!=0
y!=0/2
y!=0
y∈R
We multiply all the terms by the denominator
5y*2y-3*2y-7=0
Wy multiply elements
10y^2-6y-7=0
a = 10; b = -6; c = -7;
Δ = b2-4ac
Δ = -62-4·10·(-7)
Δ = 316
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:
$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{79}}{2*10}=\frac{6-2\sqrt{79}}{20} $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{79}}{2*10}=\frac{6+2\sqrt{79}}{20} $

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