9/10y=-19/20y+5

Solution for 9/10y=-19/20y+5 equation:

9/10y=-19/20y+5

We move all terms to the left:

9/10y-(-19/20y+5)=0


Domain of the equation: 10y!=0

y!=0/10

y!=0

y∈R



Domain of the equation: 20y+5)!=0

y∈R


We get rid of parentheses

9/10y+19/20y-5=0

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

370y-5*200y^2=0

Wy multiply elements

-1000y^2+370y=0

a = -1000; b = 370; c = 0;
Δ = b2-4ac
Δ = 3702-4·(-1000)·0
Δ = 136900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{136900}=370$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(370)-370}{2*-1000}=\frac{-740}{-2000}
=37/100
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(370)+370}{2*-1000}=\frac{0}{-2000}
=0
$