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

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

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

We move all terms to the left:

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


Domain of the equation: 10y!=0

y!=0/10

y!=0

y∈R



Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

1/10y+4/5y-5=0

We calculate fractions


5y/50y^2+40y/50y^2-5=0

We multiply all the terms by the denominator


5y+40y-5*50y^2=0

We add all the numbers together, and all the variables

45y-5*50y^2=0

Wy multiply elements

-250y^2+45y=0

a = -250; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·(-250)·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45}{2*-250}=\frac{-90}{-500}
=9/50
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*-250}=\frac{0}{-500}
=0
$