13/10y+1/20y-7/4=4/5

Solution for 13/10y+1/20y-7/4=4/5 equation:

13/10y+1/20y-7/4=4/5

We move all terms to the left:

13/10y+1/20y-7/4-(4/5)=0


Domain of the equation: 10y!=0

y!=0/10

y!=0

y∈R



Domain of the equation: 20y!=0

y!=0/20

y!=0

y∈R


We add all the numbers together, and all the variables

13/10y+1/20y-7/4-(+4/5)=0

We get rid of parentheses

13/10y+1/20y-7/4-4/5=0

We calculate fractions


(-14000y^2)/16000y^2+(-6400y^2)/16000y^2+20800y/16000y^2+800y/16000y^2=0

We multiply all the terms by the denominator


(-14000y^2)+(-6400y^2)+20800y+800y=0

We add all the numbers together, and all the variables

(-14000y^2)+(-6400y^2)+21600y=0

We get rid of parentheses

-14000y^2-6400y^2+21600y=0

We add all the numbers together, and all the variables

-20400y^2+21600y=0

a = -20400; b = 21600; c = 0;
Δ = b2-4ac
Δ = 216002-4·(-20400)·0
Δ = 466560000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{466560000}=21600$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21600)-21600}{2*-20400}=\frac{-43200}{-40800}
=1+1/17
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21600)+21600}{2*-20400}=\frac{0}{-40800}
=0
$