13/5*y=5

Solution for 13/5*y=5 equation:

13/5*y=5

We move all terms to the left:

13/5*y-(5)=0


Domain of the equation: 5*y!=0

y!=0/1

y!=0

y∈R


We multiply all the terms by the denominator


-5*5*y+13=0

Wy multiply elements

-25y*y+13=0

Wy multiply elements

-25y^2+13=0

a = -25; b = 0; c = +13;
Δ = b2-4ac
Δ = 02-4·(-25)·13
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{13}}{2*-25}=\frac{0-10\sqrt{13}}{-50}
=-\frac{10\sqrt{13}}{-50}
=-\frac{\sqrt{13}}{-5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{13}}{2*-25}=\frac{0+10\sqrt{13}}{-50}
=\frac{10\sqrt{13}}{-50}
=\frac{\sqrt{13}}{-5}
$