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

Solution for 2/5y-4+7-9/10y=0 equation:

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!=0/10

y!=0

y∈R


We add all the numbers together, and all the variables

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

We calculate fractions


20y/50y^2+(-45y)/50y^2+3=0

We multiply all the terms by the denominator


20y+(-45y)+3*50y^2=0

Wy multiply elements

150y^2+20y+(-45y)=0

We get rid of parentheses

150y^2+20y-45y=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{0}{300}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*150}=\frac{50}{300}
=1/6
$