2/5y-4=7-9/10y

Solution for 2/5y-4=7-9/10y equation:

2/5y-4=7-9/10y

We move all terms to the left:

2/5y-4-(7-9/10y)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 10y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

2/5y-(-9/10y+7)-4=0

We get rid of parentheses

2/5y+9/10y-7-4=0

We calculate fractions


20y/50y^2+45y/50y^2-7-4=0

We add all the numbers together, and all the variables

20y/50y^2+45y/50y^2-11=0

We multiply all the terms by the denominator


20y+45y-11*50y^2=0

We add all the numbers together, and all the variables

65y-11*50y^2=0

Wy multiply elements

-550y^2+65y=0

a = -550; b = 65; c = 0;
Δ = b2-4ac
Δ = 652-4·(-550)·0
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-65}{2*-550}=\frac{-130}{-1100}
=13/110
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+65}{2*-550}=\frac{0}{-1100}
=0
$