15/2y-y=13

Solution for 15/2y-y=13 equation:

15/2y-y=13

We move all terms to the left:

15/2y-y-(13)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

-1y+15/2y-13=0

We multiply all the terms by the denominator


-1y*2y-13*2y+15=0

Wy multiply elements

-2y^2-26y+15=0

a = -2; b = -26; c = +15;
Δ = b2-4ac
Δ = -262-4·(-2)·15
Δ = 796
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:

$\sqrt{\Delta}=\sqrt{796}=\sqrt{4*199}=\sqrt{4}*\sqrt{199}=2\sqrt{199}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{199}}{2*-2}=\frac{26-2\sqrt{199}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{199}}{2*-2}=\frac{26+2\sqrt{199}}{-4}
$