9/10y-3=19/20y+2

Solution for 9/10y-3=19/20y+2 equation:

9/10y-3=19/20y+2

We move all terms to the left:

9/10y-3-(19/20y+2)=0


Domain of the equation: 10y!=0

y!=0/10

y!=0

y∈R



Domain of the equation: 20y+2)!=0

y∈R


We get rid of parentheses

9/10y-19/20y-2-3=0

We calculate fractions


180y/200y^2+(-190y)/200y^2-2-3=0

We add all the numbers together, and all the variables

180y/200y^2+(-190y)/200y^2-5=0

We multiply all the terms by the denominator


180y+(-190y)-5*200y^2=0

Wy multiply elements

-1000y^2+180y+(-190y)=0

We get rid of parentheses

-1000y^2+180y-190y=0

We add all the numbers together, and all the variables

-1000y^2-10y=0

a = -1000; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-1000)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-1000}=\frac{0}{-2000}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-1000}=\frac{20}{-2000}
=-1/100
$