y-4/5y=11

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}
$