13y/3y+y=25

Solution for 13y/3y+y=25 equation:

13y/3y+y=25

We move all terms to the left:

13y/3y+y-(25)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

y+13y/3y-25=0

We multiply all the terms by the denominator


y*3y+13y-25*3y=0

We add all the numbers together, and all the variables

13y+y*3y-25*3y=0

Wy multiply elements

3y^2+13y-75y=0

We add all the numbers together, and all the variables

3y^2-62y=0

a = 3; b = -62; c = 0;
Δ = b2-4ac
Δ = -622-4·3·0
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-62}{2*3}=\frac{0}{6}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+62}{2*3}=\frac{124}{6}
=20+2/3
$