1/5y+7=17-1/20y

Solution for 1/5y+7=17-1/20y equation:

1/5y+7=17-1/20y

We move all terms to the left:

1/5y+7-(17-1/20y)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 20y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

1/5y-(-1/20y+17)+7=0

We get rid of parentheses

1/5y+1/20y-17+7=0

We calculate fractions


20y/100y^2+5y/100y^2-17+7=0

We add all the numbers together, and all the variables

20y/100y^2+5y/100y^2-10=0

We multiply all the terms by the denominator


20y+5y-10*100y^2=0

We add all the numbers together, and all the variables

25y-10*100y^2=0

Wy multiply elements

-1000y^2+25y=0

a = -1000; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-1000)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-1000}=\frac{-50}{-2000}
=1/40
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-1000}=\frac{0}{-2000}
=0
$