y-4/5y=11

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Solution for y-4/5y=11 equation:



y-4/5y=11
We move all terms to the left:
y-4/5y-(11)=0
Domain of the equation: 5y!=0
y!=0/5
y!=0
y∈R
We multiply all the terms by the denominator
y*5y-11*5y-4=0
Wy multiply elements
5y^2-55y-4=0
a = 5; b = -55; c = -4;
Δ = b2-4ac
Δ = -552-4·5·(-4)
Δ = 3105
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:
$\sqrt{\Delta}=\sqrt{3105}=\sqrt{9*345}=\sqrt{9}*\sqrt{345}=3\sqrt{345}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-3\sqrt{345}}{2*5}=\frac{55-3\sqrt{345}}{10} $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+3\sqrt{345}}{2*5}=\frac{55+3\sqrt{345}}{10} $

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