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

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

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

We move all terms to the left:

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


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

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

We calculate fractions


20y^2/100y^2+40y/100y^2+(-150y)/100y^2=0

We multiply all the terms by the denominator


20y^2+40y+(-150y)=0

We get rid of parentheses

20y^2+40y-150y=0

We add all the numbers together, and all the variables

20y^2-110y=0

a = 20; b = -110; c = 0;
Δ = b2-4ac
Δ = -1102-4·20·0
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-110}{2*20}=\frac{0}{40}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+110}{2*20}=\frac{220}{40}
=5+1/2
$