y-4/5y=13

Solution for y-4/5y=13 equation:

y-4/5y=13

We move all terms to the left:

y-4/5y-(13)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We multiply all the terms by the denominator


y*5y-13*5y-4=0

Wy multiply elements

5y^2-65y-4=0

a = 5; b = -65; c = -4;
Δ = b2-4ac
Δ = -652-4·5·(-4)
Δ = 4305
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-\sqrt{4305}}{2*5}=\frac{65-\sqrt{4305}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+\sqrt{4305}}{2*5}=\frac{65+\sqrt{4305}}{10}
$