2/5y-5/8y=5/13

Solution for 2/5y-5/8y=5/13 equation:

2/5y-5/8y=5/13

We move all terms to the left:

2/5y-5/8y-(5/13)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R


We add all the numbers together, and all the variables

2/5y-5/8y-(+5/13)=0

We get rid of parentheses

2/5y-5/8y-5/13=0

We calculate fractions


(-1600y^2)/520y^2+208y/520y^2+(-325y)/520y^2=0

We multiply all the terms by the denominator


(-1600y^2)+208y+(-325y)=0

We get rid of parentheses

-1600y^2+208y-325y=0

We add all the numbers together, and all the variables

-1600y^2-117y=0

a = -1600; b = -117; c = 0;
Δ = b2-4ac
Δ = -1172-4·(-1600)·0
Δ = 13689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13689}=117$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-117)-117}{2*-1600}=\frac{0}{-3200}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-117)+117}{2*-1600}=\frac{234}{-3200}
=-117/1600
$