13/y-10y=15

Solution for 13/y-10y=15 equation:

13/y-10y=15

We move all terms to the left:

13/y-10y-(15)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

-10y+13/y-15=0

We multiply all the terms by the denominator


-10y*y-15*y+13=0

We add all the numbers together, and all the variables

-15y-10y*y+13=0

Wy multiply elements

-10y^2-15y+13=0

a = -10; b = -15; c = +13;
Δ = b2-4ac
Δ = -152-4·(-10)·13
Δ = 745
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{-(-15)-\sqrt{745}}{2*-10}=\frac{15-\sqrt{745}}{-20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{745}}{2*-10}=\frac{15+\sqrt{745}}{-20}
$