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

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

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

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


-3y*10y+(-5y)+(-2y)-3*10y=0

Wy multiply elements

-30y^2+(-5y)+(-2y)-30y=0

We get rid of parentheses

-30y^2-5y-2y-30y=0

We add all the numbers together, and all the variables

-30y^2-37y=0

a = -30; b = -37; c = 0;
Δ = b2-4ac
Δ = -372-4·(-30)·0
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-37}{2*-30}=\frac{0}{-60}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+37}{2*-30}=\frac{74}{-60}
=-1+7/30
$