4/5y-2=3/10y+1

Solution for 4/5y-2=3/10y+1 equation:

4/5y-2=3/10y+1

We move all terms to the left:

4/5y-2-(3/10y+1)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 10y+1)!=0

y∈R


We get rid of parentheses

4/5y-3/10y-1-2=0

We calculate fractions


40y/50y^2+(-15y)/50y^2-1-2=0

We add all the numbers together, and all the variables

40y/50y^2+(-15y)/50y^2-3=0

We multiply all the terms by the denominator


40y+(-15y)-3*50y^2=0

Wy multiply elements

-150y^2+40y+(-15y)=0

We get rid of parentheses

-150y^2+40y-15y=0

We add all the numbers together, and all the variables

-150y^2+25y=0

a = -150; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-150)·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*-150}=\frac{-50}{-300}
=1/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-150}=\frac{0}{-300}
=0
$