3/20y-9/5y+8/5=13/10

Solution for 3/20y-9/5y+8/5=13/10 equation:

3/20y-9/5y+8/5=13/10

We move all terms to the left:

3/20y-9/5y+8/5-(13/10)=0


Domain of the equation: 20y!=0

y!=0/20

y!=0

y∈R



Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

3/20y-9/5y+8/5-(+13/10)=0

We get rid of parentheses

3/20y-9/5y+8/5-13/10=0

We calculate fractions


(-32500y^2)/25000y^2+3750y/25000y^2+(-1800y)/25000y^2+1600y/25000y^2=0

We multiply all the terms by the denominator


(-32500y^2)+3750y+(-1800y)+1600y=0

We add all the numbers together, and all the variables

(-32500y^2)+5350y+(-1800y)=0

We get rid of parentheses

-32500y^2+5350y-1800y=0

We add all the numbers together, and all the variables

-32500y^2+3550y=0

a = -32500; b = 3550; c = 0;
Δ = b2-4ac
Δ = 35502-4·(-32500)·0
Δ = 12602500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12602500}=3550$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3550)-3550}{2*-32500}=\frac{-7100}{-65000}
=71/650
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3550)+3550}{2*-32500}=\frac{0}{-65000}
=0
$