1/5y+7=22-1/20y

Solution for 1/5y+7=22-1/20y equation:

1/5y+7=22-1/20y

We move all terms to the left:

1/5y+7-(22-1/20y)=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+22)+7=0

We get rid of parentheses

1/5y+1/20y-22+7=0

We calculate fractions


20y/100y^2+5y/100y^2-22+7=0

We add all the numbers together, and all the variables

20y/100y^2+5y/100y^2-15=0

We multiply all the terms by the denominator


20y+5y-15*100y^2=0

We add all the numbers together, and all the variables

25y-15*100y^2=0

Wy multiply elements

-1500y^2+25y=0

a = -1500; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-1500)·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*-1500}=\frac{-50}{-3000}
=1/60
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-1500}=\frac{0}{-3000}
=0
$