4/5y-2=9/10y+3

Solution for 4/5y-2=9/10y+3 equation:

4/5y-2=9/10y+3

We move all terms to the left:

4/5y-2-(9/10y+3)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 10y+3)!=0

y∈R


We get rid of parentheses

4/5y-9/10y-3-2=0

We calculate fractions


40y/50y^2+(-45y)/50y^2-3-2=0

We add all the numbers together, and all the variables

40y/50y^2+(-45y)/50y^2-5=0

We multiply all the terms by the denominator


40y+(-45y)-5*50y^2=0

Wy multiply elements

-250y^2+40y+(-45y)=0

We get rid of parentheses

-250y^2+40y-45y=0

We add all the numbers together, and all the variables

-250y^2-5y=0

a = -250; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-250)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-250}=\frac{0}{-500}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-250}=\frac{10}{-500}
=-1/50
$